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Partnership and Discount

মোট প্রশ্ন৪৪৪এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Partnership and Discount

PrepBank · পাতা ১ / ৫ · ১–১০০ / ৪৪৪

১.
A shopkeeper marks his goods 30% above the cost price and offers a discount of 10% on the marked price. What is his gain percent?
  1. ক
    25%
  2. খ
    20%
  3. গ
    17%
  4. ঘ
    15%
সঠিক উত্তর: গ
17%
উত্তর
সঠিক উত্তর: গ
17%
গ
ব্যাখ্যা
Question: A shopkeeper marks his goods 30% above the cost price and offers a discount of 10% on the marked price. What is his gain percent?

Solution: 
Let,
the cost price (CP) be Tk. 100

Marked Price = 30% more than cost price
= 100 + 30
= 130 Tk.

Discount = 10% of 130
= (10/100) ​× 130
=13 Tk.

Selling Price (SP)= 130 - 13 = 117 Tk.

∴ Profit = SP - CP = 117 - 100 = 17 Tk.

∴ Gain percent = 17%
২.
Abir and Asif started a business investing Tk. 27500 and Tk. 35000 respectively. Out of a total profit of Tk. 14200, Asif's share is?
  1. ক
    ক) Tk. 6248
  2. খ
    খ) Tk. 7950
  3. গ
    গ) Tk. 7952
  4. ঘ
    ঘ) Tk. 6250
সঠিক উত্তর: গ
গ) Tk. 7952
উত্তর
সঠিক উত্তর: গ
গ) Tk. 7952
গ
ব্যাখ্যা
Question: Abir and Asif started a business investing Tk. 27500 and Tk. 35000 respectively. Out of a total profit of Tk. 14200, Asif's share is?

Solution:
Given,
Investment ratio = 27500 : 35000
= 11 : 14
Sum of the ratio's = 11 + 14 = 25

∴ Asif's share = 14200 × (14/25)
= 7952
৩.
A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?
  1. ক
    3 months
  2. খ
    6 months
  3. গ
    10 months
  4. ঘ
    12 months
  5. ঙ
    5 months
সঠিক উত্তর: গ
10 months
উত্তর
সঠিক উত্তর: গ
10 months
গ
ব্যাখ্যা
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?

Solution:
Let the total profit be Tk. z.
Then,
B's share = Tk. 2z/3,
A's share = Tk. z - (2z/3 ) = Tk. z/3.

A : B = z/3 : 2z/3 = 1 : 2

Let the total capital be Tk. x and suppose B's money was used for y months. Then.
{(x/ 4) × 15}/{(3x/4) × y} = 1/2
⇒ y = (15 × 2)/3 = 10 .

Thus, B's money was used for 10 months.
৪.
Abir and Babul invest in a business in the ratio 5 : 4. If 10% of the total profit goes to charity and abir’s share is Tk 945, the total profit is -
  1. ক
    1500 tk
  2. খ
    2100 tk
  3. গ
    1890 tk
  4. ঘ
    2400 tk
সঠিক উত্তর: গ
1890 tk
উত্তর
সঠিক উত্তর: গ
1890 tk
গ
ব্যাখ্যা
Question: Abir and Babul invest in a business in the ratio 5 : 4. If 10% of the total profit goes to charity and abir’s share is Tk 945, the total profit is -  

Solution:
Let,
The total profit = 100 tk

After paying 10% to charity,
Abir’s share = 90 × (5/9)
= 50 tk

Now,
If abir’s share is tk 50, total profit = 100 tk
If abir’s share is tk 1, total profit = 100/50 tk
If abir’s share is tk 945, total profit = (100/50) × 945
= 1890 tk

So, the total profit is 1890 tk.
৫.
A company issued 20000 shares of par value Tk. 10 each. If the total dividend declared by the company is Tk. 24000, find the rate of dividend paid by the company.
  1. ক
    ক) 12%
  2. খ
    খ) 10%
  3. গ
    গ) 9%
  4. ঘ
    ঘ) 15%
সঠিক উত্তর: ক
ক) 12%
উত্তর
সঠিক উত্তর: ক
ক) 12%
ক
ব্যাখ্যা
Number of shares = 20000
Face value of each share = Tk. 10
dividend per share = (10 × R/100) where R is the Rate of interest.
Total dividend = 20000 ×10 ×R/100
20000 ×10 ×R/100 = 24000
R = 24000/2000
= 12
Hence the dividend is 12%.
৬.
A and B invest in a business in the ratio 6 : 4. If 10% of the total profit goes to charity and A's share is Tk. 378, what is the total profit?
  1. ক
    ক) Tk. 700
  2. খ
    খ) Tk. 600
  3. গ
    গ) Tk. 500
  4. ঘ
    ঘ) Tk. 400
সঠিক উত্তর: ক
ক) Tk. 700
উত্তর
সঠিক উত্তর: ক
ক) Tk. 700
ক
ব্যাখ্যা
Question: A and B invest in a business in the ratio 6 : 4. If 10% of the total profit goes to charity and A's share is Tk. 378, what is the total profit?

Solution:
Let,
The total profit be Tk. 100.
After paying 10% to charity,
A's share = 90 × (6/10)  = Tk. 54

If A's share is Tk. 54, total profit = Tk. 100.
If A's share is Tk. 1, total profit = Tk. 100/54
∴ If A's share is Tk. 378, total profit = Tk. (100 × 378)/54
= Tk. 700
৭.
A, B and C enter into a partnership investing Tk 2100, Tk 2700 and Tk 3300. Find the their respective shares in annual profit of 40,500.
  1. ক
    10500, 13500, 18500
  2. খ
    10500, 13500, 17500
  3. গ
    10500, 13500, 16500
  4. ঘ
    10500, 13500, 19500
সঠিক উত্তর: গ
10500, 13500, 16500
উত্তর
সঠিক উত্তর: গ
10500, 13500, 16500
গ
ব্যাখ্যা
A : B : C = 2100 : 2700 : 3300 = 7 : 9 : 11
Sum of the ratio = 7 + 9 + 11 = 27
Therefore, A's share = (7/27) × 40500 = Tk 10500
B's share = (9/27) × 40500 = Tk 13500
and C's share = (11/27)× 40500 = Tk 16500
৮.
Shakil started a software business by investing Tk. 20000. After six months, Neel joined him with a capital of Tk. 30000. After 3 years, they earned a profit of Tk. 13950. What was Shakil’s share in the profit?
  1. ক
    Tk. 6200
  2. খ
    Tk. 6400
  3. গ
    Tk. 4200
  4. ঘ
    Tk. 7750
সঠিক উত্তর: ক
Tk. 6200
উত্তর
সঠিক উত্তর: ক
Tk. 6200
ক
ব্যাখ্যা
Question: Shakil started a software business by investing Tk. 20000. After six months, Neel joined him with a capital of Tk. 30000. After 3 years, they earned a profit of Tk. 13950. What was Shakil’s share in the profit?

Solution:
Ratio of capitals of Shakil and Neel
= (20000 × 36) : (30000 × 30)
= 720000 : 900000
= 4 : 5.

Shakil’s share is = Tk. 13950 × (4/9) = Tk. 6200.
৯.
P, Q, R three friends invested in a business. Q invested twice of R and P invested half of R. what is the profit ratio of Q, P, R?
  1. ক
    ক) 2 : 1 : 4
  2. খ
    খ) 1 : 4 : 2
  3. গ
    গ) 4 : 1 : 2
  4. ঘ
    ঘ) 4 : 2 : 1
সঠিক উত্তর: গ
গ) 4 : 1 : 2
উত্তর
সঠিক উত্তর: গ
গ) 4 : 1 : 2
গ
ব্যাখ্যা
Question: P, Q, R three friends invested in a business. Q invested twice of R and P invested half of R. what is the profit ratio of Q, P, R?

Solution: 
Let P invested x 
Then,
investment of R is 2x and
Investment of Q is (2 × 2x) or, 4x

∴ The profit ratio of Q, P, R will be 4x : x : 2x = 4 : 1 : 2
১০.
Aysha and Jara started a business by investing Tk. 85000 and Tk. 15000 each. What be will the ratio of profit earned after 2 years between Aysha and Jara respectively?
  1. ক
    9 : 8
  2. খ
    17 : 5
  3. গ
    5 : 4
  4. ঘ
    17 : 3
সঠিক উত্তর: ঘ
17 : 3
উত্তর
সঠিক উত্তর: ঘ
17 : 3
ঘ
ব্যাখ্যা

Question: Aysha and Jara started a business by investing Tk. 85000 and Tk. 15000 each. What be will the ratio of profit earned after 2 years between Aysha and Jara respectively?

Solution:
Given,
Aysha's investment = Tk. 85,000
Jara's investment = Tk. 15,000
Time = 2 years for both

The ratio of profit earned after 2 years between Aysha and Jara respectively = (85000 × 2) : (15000 × 2)
= 170000 : 30000
= 17 : 3

১১.
A, B and C enter into partnership by making investments in the ratio of 3 : 5 : 7. After a year, C invests another Tk. 337600 while A withdraws Tk.45600. The ratio of investments then changes to 24 : 59 : 67. How much did A invest initially?
  1. ক
    ক) 10000
  2. খ
    খ) 12000
  3. গ
    গ) 141600
  4. ঘ
    ঘ) 14900
  5. ঙ
    ঙ) None Of the Above
সঠিক উত্তর: গ
গ) 141600
উত্তর
সঠিক উত্তর: গ
গ) 141600
গ
ব্যাখ্যা

Let, A : B : C = 3x : 5x : 7x
After 1 year C investment = 7x + 337600
After 1 year A investment = 3x - 45,600
ATQ,
(3x − 45600)/5x = 24/59
=> 59 × (3x - 45,600) = 120x
=> 177x - 120x = 45600 × 59
=> 57x = 45600 × 59
=> x = 800 × 59 = 47,200
A's initial investment was = 47,200 × 3 = 141600 [Answer.]

১২.
Kavita bought land for Tk. 50000. She sold the land by offering a 30% discount on the land. Find how much did she lose.
  1. ক
    Tk. 15000
  2. খ
    Tk. 12000
  3. গ
    Tk. 18000
  4. ঘ
    Tk. 20000
সঠিক উত্তর: ক
Tk. 15000
উত্তর
সঠিক উত্তর: ক
Tk. 15000
ক
ব্যাখ্যা
Question: Kavita bought land for Tk. 50000. She sold the land by offering a 30% discount on the land. Find how much did she lose.

Solution:
Principal amount p = 50000
Discount rate, r = 30%

Total Discount = 50000 × (30/100) 
= 15000

Thus, Selling price = 50000 - 15000 = 35000
Hence, Kavitha lost Tk. 15000
১৩.
A retailer, while selling a watch, was asking for such a price that would allow him to offer a 10% discount and still make a profit of 20% on cost. If the cost of the watch was Tk. 1,200, what was his asking price?
  1. ক
    Tk. 1,400
  2. খ
    Tk. 1,600
  3. গ
    Tk. 1,800
  4. ঘ
    Tk. 1,700
  5. ঙ
    None of these
সঠিক উত্তর: খ
Tk. 1,600
উত্তর
সঠিক উত্তর: খ
Tk. 1,600
খ
ব্যাখ্যা

Question: A retailer, while selling a watch, was asking for such a price that would allow him to offer a 10% discount and still make a profit of 20% on cost. If the cost of the watch was Tk. 1,200, what was his asking price?

Solution:
প্রথম ধাপে, 20% লাভে ঘড়িটির বিক্রয়মূল্য (Selling Price) নির্ণয় করতে হবে।
ক্রয়মূল্য = 1,200 টাকা
বিক্রয়মূল্য = 1,200 + (1,200 এর 20%)
= 1,200 + 240 = 1,440 টাকা

এখন, দ্বিতীয় ধাপে, 10% ছাড়ের ওপর ভিত্তি করে ধার্যমূল্য (Asking Price) নির্ণয় করতে হবে।
যদি ধার্যমূল্য 100 টাকা হয়, তবে 10% ছাড়ে বিক্রয়মূল্য হবে (100 - 10) = 90 টাকা।

বিক্রয়মূল্য 90 টাকা হলে, ধার্যমূল্য = 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে, ধার্যমূল্য = 100/90 টাকা
বিক্রয়মূল্য 1,440 টাকা হলে, ধার্যমূল্য = (100/90) × 1,440 = 1,600 টাকা

∴ ঘড়িটির ধার্যমূল্য বা Asking Price ছিল 1,600 টাকা।

১৪.
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk 1425, the total profit is-
  1. ক
    ক) 1500 Tk
  2. খ
    খ) 2000 Tk
  3. গ
    গ) 2500 Tk
  4. ঘ
    ঘ) 3000 Tk
সঠিক উত্তর: গ
গ) 2500 Tk
উত্তর
সঠিক উত্তর: গ
গ) 2500 Tk
গ
ব্যাখ্যা
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk 1425, the total profit is-

Solution:
Let the total profit be 100
After paying to charity, A's share =Tk (95 × 3/5) = Tk 57

If A's share is Tk 57, Total profit = Tk 100
If A's share Tk 1425 ,Total profit = (100/57) × 1425 = 2500
১৫.
A man spends one-quarter of his income on food. One-fifth of it on rent and remaining which is Tk. 517 on other commodities. What is his total income? 
  1. ক
    ক) Tk. 890 
  2. খ
    খ) Tk. 925 
  3. গ
    গ) Tk. 940 
  4. ঘ
    ঘ) Tk. 965 
সঠিক উত্তর: গ
গ) Tk. 940 
উত্তর
সঠিক উত্তর: গ
গ) Tk. 940 
গ
ব্যাখ্যা
Question: A man spends one-quarter of his income on food. One-fifth of it on rent and remaining which is Tk. 517 on other commodities. What is his total income? 

Solution: 
Let the total income be Tk. x
Then remaining money,
x - {(x/4) + (x/5)} 
= x - (9x/20) 
= 11x/20

ATQ,
11x/20 = 517
⇒ x = (517 × 20)/11
⇒ x = 47 × 20
∴ x = 940 

∴ His total income is Tk. 940
১৬.
A, B, C enter into partnership, A invests 3 times as much as B invests and B invests two third of what C invests. At the end of the year, profit earned is Tk. 6,600. What is the share of B?
  1. ক
    ক) 1,100
  2. খ
    খ) 1,150
  3. গ
    গ) 1,175
  4. ঘ
    ঘ) 1,200
সঠিক উত্তর: ঘ
ঘ) 1,200
উত্তর
সঠিক উত্তর: ঘ
ঘ) 1,200
ঘ
ব্যাখ্যা
ধরি,
C বিনিয়োগ করে x টাকা 
B বিনিয়োগ করে (x এর 2/3) টাকা 
                          = 2x/3 টাকা 
A বিনিয়োগ করে {3 × (2x/3)} টাকা 
                          =2x টাকা 

A , B এবং C এর বিনিয়োগের অনুপাত = 2x : (2x/3) : x
                                                           = 2 : (2/3) : 1
                                                            = 6 : 2 : 3 
বিনিয়োগের অনুপাতের যোগফল = 6 + 2 + 3 = 11 

B লাভ পাবে = (6,600 এর 2/11) = 1200 টাকা
১৭.
Asif and Rasel take 9 days to do a particular job. Asif takes 18 days to do the job alone. In how many days can Rasel do the job alone?
  1. ক
    ক) 12 days
  2. খ
    খ) 15 days
  3. গ
    গ) 18 days
  4. ঘ
    ঘ) 20 days
সঠিক উত্তর: গ
গ) 18 days
উত্তর
সঠিক উত্তর: গ
গ) 18 days
গ
ব্যাখ্যা
Question: Asif and Rasel take 9 days to do a particular job. Asif takes 18 days to do the job alone. In how many days can Rasel do the job alone? 

Solution: 
১৮ দিনে আসিফ করে সম্পূর্ণ বা ১ অংশ
∴ ১ দিনে আসিফ করে ১/১৮ অংশ
∴ ৯ দিনে আসিফ করে ৯/১৮ অংশ = ১/২ অংশ 

∴ রাসেল ৯ দিনে করে (১ - ১/২) অংশ = ১/২ অংশ 

রাসেল ১/২ অংশ করে ৯ দিনে 
∴ রাসেল ১ বা সম্পূর্ণ অংশ করে (৯ × ২) দিনে = ১৮ দিনে
১৮.
Three persons stared a placement business with a capital of Tk. 3000. B invests Tk. 600 less than A and C invests Tk. 300 less than B. What is B's share in a profit of Tk. 886 ?
  1. ক
    ক) Tk. 255.50
  2. খ
    খ) Tk. 265.80
  3. গ
    গ) Tk. 245.70
  4. ঘ
    ঘ) Tk. 275.90
সঠিক উত্তর: খ
খ) Tk. 265.80
উত্তর
সঠিক উত্তর: খ
খ) Tk. 265.80
খ
ব্যাখ্যা
Let
A's capital = Tk. x
Then, B's capital = Tk. (x - 600)
C's capital = Tk.(x - 600) - 300 = Tk. (x - 900)
∴ x + (x - 600) + (x - 900) = 3000
⇒ 3x = 4500
⇒ x = 1500
A's capital = Tk. 1500
B's capital = Tk. (1500 - 600) = Tk.900
C's capital = Tk. (1500 - 900) = Tk.600

So, A : B : C=1500 : 900 : 600
                  =5 : 3 : 2

Hence, B's share= Tk.(886 × 3/10)
                          = Tk. 265.80
১৯.
A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English?
  1. ক
    ক) 72
  2. খ
    খ) 69
  3. গ
    গ) 66
  4. ঘ
    ঘ) 78
সঠিক উত্তর: গ
গ) 66
উত্তর
সঠিক উত্তর: গ
গ) 66
গ
ব্যাখ্যা
Total marks obtained by the student = 55% of 800
= {(55/100) × 800}
= 440
 ∴ Marks scored in English
= 15% of 440
= {(15/100) × 440}
= 66
২০.
A starts a business with Tk 4,500. After 4 months, B joins as a partner by investing some amount. At the end of one year from the start, the profits are shared in the ratio A : B = 3 : 4. Find B’s capital investment.
  1. ক
    8000 TK
  2. খ
    10,000 TK
  3. গ
    12,000 TK
  4. ঘ
    9000 TK
সঠিক উত্তর: ঘ
9000 TK
উত্তর
সঠিক উত্তর: ঘ
9000 TK
ঘ
ব্যাখ্যা

Question : A starts a business with Tk 4,500. After 4 months, B joins as a partner by investing some amount. At the end of one year from the start, the profits are shared in the ratio A : B = 3 : 4. Find B’s capital investment.

Solution:
Let,
B's capital be TK X
Then,
(4500 × 12)/8X = 3/4
⇒ 24X = (4500 × 12 × 4)
⇒ 24X = 216,000
⇒ X = 216,000/24
∴ X = 9000

২১.
Rina and Mina invest Tk. 25,000 and Tk. 35,000 respectively in a partnership. They earned a profit of Tk. 9,000. Find Rina’s share of the profit.
  1. ক
    Tk. 4725
  2. খ
    Tk. 4575
  3. গ
    Tk. 4025
  4. ঘ
    Tk. 3750
সঠিক উত্তর: ঘ
Tk. 3750
উত্তর
সঠিক উত্তর: ঘ
Tk. 3750
ঘ
ব্যাখ্যা
Question: Rina and Mina invest Tk. 25,000 and Tk. 35,000 respectively in a partnership. They earned a profit of Tk. 9,000. Find Rina’s share of the profit.

Solution:
Given,
Investment ratio = 25000 : 35000
= 5 : 7

Sum of the ratio's = 5 + 7 = 12

∴ Rina's share = 9000 × (5/12)
= Tk. 3750
২২.
A restaurant owner allows employees to purchase meals for 28% off list price. An employee purchases a meal with a list price of Tk. 16.50.  What does she pay for the meal?
  1. ক
    Tk. 11.88
  2. খ
    Tk. 12.06
  3. গ
    Tk. 13.20
  4. ঘ
    Tk. 12.40
সঠিক উত্তর: ক
Tk. 11.88
উত্তর
সঠিক উত্তর: ক
Tk. 11.88
ক
ব্যাখ্যা
Question: A restaurant owner allows employees to purchase meals for 28% off list price. An employee purchases a meal with a list price of Tk. 16.50.  What does she pay for the meal?

Solution:
If she gets a 28% discount, she pays 72% of the list price:

∴ Amount to be paid = (72/100) × 16.50
= 11.88
২৩.
Rana sells 40 shares in a company via a stock broker who charges a flat Tk. 20 commission rate on all transactions under Tk. 1000. His bank account is credited with Tk. 692 from the sale of the shares. What price were his shares sold at?
  1. ক
    ক) Tk. 15.5
  2. খ
    খ) Tk. 21.5
  3. গ
    গ) Tk. 19.5
  4. ঘ
    ঘ) Tk. 17.8
সঠিক উত্তর: ঘ
ঘ) Tk. 17.8
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. 17.8
ঘ
ব্যাখ্যা
কমিশনসহ রেজার শেয়ারের বিক্রয়মূল্য ৬৯২+২০ = ৭১২ টাকা।
তাহলে ৪০ শেয়ারের বিক্রয়মূল্য ৭১২/৪০ = ১৭.৮।
২৪.
A sales representative sells goods worth Tk. 22,000. If his commission rate is 12.5%, what is the amount of commission he earns?
  1. ক
    2750
  2. খ
    2820
  3. গ
    3560
  4. ঘ
    3550
সঠিক উত্তর: ক
2750
উত্তর
সঠিক উত্তর: ক
2750
ক
ব্যাখ্যা

Question: A sales representative sells goods worth Tk. 22,000. If his commission rate is 12.5%, what is the amount of commission he earns?

Solution:
Commission = 12.5% of 22000
= (125/10) × (1/100) × 22000
= (125/1000) × 22000
= 2750

২৫.
A and B started a business by investing Tk. 4000 and Tk. 5000 respectively. Find the A's share out of a total profit of Tk. 1800.
  1. ক
    ক) Tk. 1200
  2. খ
    খ) Tk. 800
  3. গ
    গ) Tk. 600
  4. ঘ
    ঘ) Tk. 1800
সঠিক উত্তর: খ
খ) Tk. 800
উত্তর
সঠিক উত্তর: খ
খ) Tk. 800
খ
ব্যাখ্যা
Ratio of A and B's investment = 4000 : 5000 = 4 : 5
A's share = 4/(4 + 5) × 1800 = Tk. 800
২৬.
A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?
  1. ক
    ক) 3 months
  2. খ
    খ) 8 months
  3. গ
    গ) 10 months
  4. ঘ
    ঘ) 11 months
সঠিক উত্তর: গ
গ) 10 months
উত্তর
সঠিক উত্তর: গ
গ) 10 months
গ
ব্যাখ্যা
প্রশ্ন: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used? 

সমাধান: 
ধরি,
মোট লাভ ক টাকা 
B লাভ করে (২ক)/৩ টাকা 
∴ A লাভ করে ১ - (২ক)/৩ টাকা
= ক/৩ টাকা 

মোট মূলধন খ টাকা 
A এর অংশ খ/৪ টাকা 
B  এর অংশ (খ - খ/৪) টাকা 
= ৩খ/৪ টাকা 

খ/৪ টাকায় ক/৩ টাকা লাভ করে ১৫ মাসে
∴ ১ টাকায় ক/৩ টাকা লাভ করে ১৫খ/৪ মাসে
∴ ১ টাকায় ১ টাকা লাভ করে (১৫খ/৪) × (৩/ক) = ৪৫খ/৪ক  মাসে
∴ ১ টাকায় (২ক)/৩ টাকা লাভ করে (৪৫খ/৪ক) × (২ক/৩) = ১৫খ/২ মাসে
∴ ৩খ/৪ টাকায় (২ক)/৩ টাকা লাভ করে (১৫খ/২) × (৪/৩খ) = ১০ মাসে 
২৭.
Mahmud got discount of 20% over the retail price of a book. He eventually saved taka 300 on his total purchase of the books. How many books did he buy if the retail price of a book is 50 taka?
  1. ক
    30 books
  2. খ
    25 books
  3. গ
    35 books
  4. ঘ
    40 books
সঠিক উত্তর: ক
30 books
উত্তর
সঠিক উত্তর: ক
30 books
ক
ব্যাখ্যা
Question: Mahmud got discount of 20% over the retail price of a book. He eventually saved taka 300 on his total purchase of the books. How many books did he buy if the retail price of a book is 50 taka?

Solution:
Given,
retail price of a book = 50 Tk.
At 20% discount,
purchase price of a book = 50 - (50 × 20%) = 40 Tk.

Saved amount per book = 50 - 40 = 10 Tk.

Now 10 Tk. is saved in = 1 book
∴ 300 Tk. is saved in = (1 × 300)/10 books
= 30 books

∴ Mahmud purchased 30 books.
২৮.
A and B invest in a business in the ratio 7 : 3. If 20% of the total profit goes to charity and B's share is TK 12000, the total profit is-
  1. ক
    30,000 taka
  2. খ
    40,000 taka
  3. গ
    50,000 taka 
  4. ঘ
    60,000 taka
সঠিক উত্তর: গ
50,000 taka 
উত্তর
সঠিক উত্তর: গ
50,000 taka 
গ
ব্যাখ্যা

Question: A and B invest in a business in the ratio 7 : 3. If 20% of the total profit goes to charity and B's share is TK 12000, the total profit is-

Solution: 
মনে করি,
মোট লাভ 100 টাকা
20% দান করার পর থাকে = (100 - 100 এর 20%) = 80 টাকা

80 টাকার মধ্যে B পাবে = 80 × (3/10) = 24 টাকা

24 টাকা পায় যখন মোট লাভ 100 টাকা
∴ 12000 টাকা পায় যখন মোট লাভ = (12000 × 100)/24 = 50,000 টাকা 

২৯.
What is the net discount for successive discounts of 20% and 30%?
  1. ক
    ক) 44%
  2. খ
    খ) 36%
  3. গ
    গ) 48%
  4. ঘ
    ঘ) 24%
সঠিক উত্তর: ক
ক) 44%
উত্তর
সঠিক উত্তর: ক
ক) 44%
ক
ব্যাখ্যা
Question: What is the net discount for successive discounts of 20% and 30%?
Solution: 
ধরি, লিখিত মূল্য  ‘x’.

20% ছাড়ের পর, 
⇒ বিক্রয়মূল্য  = x - 0.2x = 0.8x

30% ছাড়ের পর,
⇒ বিক্রয়মূল্য = 0.8x - 0.8 × 0.3x = 0.56x

∴ মোট ছাড় = [(x - 0.56x)/x] × 100 = 44%
৩০.
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months, and 7 months respectively. What was the ratio of their investment?
  1. ক
    5 : 7 : 8
  2. খ
    20 : 49 : 64
  3. গ
    38 : 28 : 21
  4. ঘ
    10 : 13 : 20
সঠিক উত্তর: খ
20 : 49 : 64
উত্তর
সঠিক উত্তর: খ
20 : 49 : 64
খ
ব্যাখ্যা

Question: Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months, and 7 months respectively. What was the ratio of their investment?

Solution:
Let their investments be
x Tk for 14 months,
y Tk for 8 months and
z Tk for 7 months respectively.

Then,
14x : 8y : 7z = 5 : 7 : 8

Now, 
14x/8y = 5/7
⇒ 98x = 40y
⇒ y = 49x/20

And,
14x/7z = 5/8
⇒ 112x = 35z
⇒ z = 16x/5

∴ x : y : z
= x : 49x/20 : 16x/5
= 20 : 49 : 64

৩১.
A, B and C enter into a partnership. A contributes one - third of the capital while B contributes as much as A and C together contribute. If the profit at the end of the year amounts to Tk. 900, What would A receive?
  1. ক
    ক) Tk 300
  2. খ
    খ) Tk 450
  3. গ
    গ) Tk 150
  4. ঘ
    ঘ) Tk 250
সঠিক উত্তর: ক
ক) Tk 300
উত্তর
সঠিক উত্তর: ক
ক) Tk 300
ক
ব্যাখ্যা
ধরি, মোট বিনিয়োগ x টাকা
A বিনিয়োগ করে x/3 টাকা
B + C = (x - x/3) = 2x/3
কিন্তু, B এর বিনিয়োগ পরিমান A ও C এর মোট বিনিয়োগের সমান।
∴ x/3 + C + C = 2x/3
⇒ 2C = 2x/3 - x/3
⇒ 2C = x/3
⇒ C = x/6 এবং B = 2x/3 - x/6 = 3x/6 = x/2

A : B : C = x/3 : x/2 : x/6 = 2 : 3 : 1

∴ A এর লাভের পরিমাণ { 900 এর 2/(2 + 3 + 1)} = (900 এর 2/6) = 300 টাকা
৩২.
Arif and Samir started a business in partnership by investing Tk. 20,000 and Tk. 15,000 respectively. After six months, Tanvir joined them with Tk. 20,000. If the total profit earned at the end of 2 years from the start of the business is Tk. 25,000, what is Samir’s share? 
  1. ক
    3,500
  2. খ
    1,500
  3. গ
    7,500
  4. ঘ
    5000
সঠিক উত্তর: গ
7,500
উত্তর
সঠিক উত্তর: গ
7,500
গ
ব্যাখ্যা

Question: Arif and Samir started a business in partnership by investing Tk. 20,000 and Tk. 15,000 respectively. After six months, Tanvir joined them with Tk. 20,000. If the total profit earned at the end of 2 years from the start of the business is Tk. 25,000, what is Samir’s share?

Solution:
Here,
Arif : Samir : Tanvir
= (20,000 x 24) : (15,000 x 24) : (20,000 x 18)
= 4 : 3 : 3.

So, Samir's share = 25000 x 3/10 = 7,500.

৩৩.
Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.
  1. ক
    3
  2. খ
    4
  3. গ
    6
  4. ঘ
    8
সঠিক উত্তর: খ
4
উত্তর
সঠিক উত্তর: খ
4
খ
ব্যাখ্যা
Question: Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.

Solution:
we can assume that Omar join into business after x months.
So Omar money was invested for (12 - x) months.

(38000 × 12)/{28500 × (12 - x)} = 2/1 (The given ratio of 16 : 8 is equivalent to 2 :1)
⇒ 456000 = 28500(12 - x) 
⇒ 456000 = 57000(12 - x)
⇒ 57(12 - x) = 456
⇒ 12 - x = 8
∴ x = 4

After 4 months Omar join the business.
৩৪.
The single discount equivalent to two successive discount of 20% and 5% is = ?
  1. ক
    ক) 24%
  2. খ
    খ) 25%
  3. গ
    গ) 22%
  4. ঘ
    ঘ) 23%
সঠিক উত্তর: ক
ক) 24%
উত্তর
সঠিক উত্তর: ক
ক) 24%
ক
ব্যাখ্যা

Two successive discount is equivalent
= 20+5− 20×5/100
= 25−1 = 24%

৩৫.
A, B and C jointly thought of engaging themeselves in a business venture. It was agreed that A would invest TK. 8000 for 7 months, B, TK. 10,000 for 4 months and C, TK. 12,000 for 3 months. A wants to be the working member for which, he was to receive 10% of the profits. The profit earned was TK. 6600. Calculate the share of C in the profit.
  1. ক
    TK. 2027
  2. খ
    TK. 1720
  3. গ
    TK. 1620
  4. ঘ
    TK. 2720
  5. ঙ
    TK. 2620
সঠিক উত্তর: গ
TK. 1620
উত্তর
সঠিক উত্তর: গ
TK. 1620
গ
ব্যাখ্যা

Question: A, B and C jointly thought of engaging themeselves in a business venture. It was agreed that A would invest TK. 8000 for 7 months, B, TK. 10,000 for 4 months and C, TK. 12,000 for 3 months. A wants to be the working member for which, he was to receive 10% of the profits. The profit earned was TK. 6600. Calculate the share of C in the profit.

Solution:
Ratio of their investments = (8000 × 7) : (10,000 × 4) : (12,000 × 3)
= 56,000 : 40,000 : 36,000
= 14 : 10 : 9

sum of ratio = (14 + 10 + 9) = 33

Here,
The profit earned was TK. 6600

For working A received = 10% of TK. 6600
= TK. (10 × 6600)/100
= TK. 660

Remaining profit = TK. (6600 - 660) = TK. 5940

∴ C's share = TK. {5940 × (9/33)
= TK. 1620

৩৬.
A, B and C enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A increases his share 50%. If the total profit at the end of one year be Tk. 21,600, then B's share in the profit is-
  1. ক
    Tk. 2100
  2. খ
    Tk. 2400
  3. গ
    Tk. 3600
  4. ঘ
    Tk. 4000
সঠিক উত্তর: ঘ
Tk. 4000
উত্তর
সঠিক উত্তর: ঘ
Tk. 4000
ঘ
ব্যাখ্যা
Question: A, B and C enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A increases his share 50%. If the total profit at the end of one year be Tk. 21,600, then B's share in the profit is-

Solution:
Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36.
Let the initial investments be 105x, 40x and 36x.

A : B : C = {105x × 4 + (150/100) × 105x × 8} : (40x × 12) : (36x × 12)
= 1680x : 480x : 432x
= 35 : 10 : 9.

Hence, B's share = Tk. 21600 × (10/54) = Tk. 4000.
৩৭.
A and B together can complete a piece of work in 12 days, B and C can do it in 20 days and C and A can do it in 15 days. A, B and C together can complete it in-
  1. ক
    ক) 12 days
  2. খ
    খ) 6 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 10 days
সঠিক উত্তর: ঘ
ঘ) 10 days
উত্তর
সঠিক উত্তর: ঘ
ঘ) 10 days
ঘ
ব্যাখ্যা

A + B can do the work in 12 days.
In a single day A + B will do 1/12th portion of the work.
B+C can do the work in 15 days.
In a single day B+C will do 1/15th portion of the work.
A + C can do the work in 20 days.
In a single day A+C will do 1/20th portion of the work.

In a day (A+B) + (A+C) + (C+A) will do = (1/12) + (1/15) + (1/20) portion of the work.
⇒ 2(A+B+C) = (1/12)+(1/15)+(1/20) = (5+4+3)/60 = 1/5 portion of the work.
Then, (A+B+C) will do = 1/10 portion of the work in a day
∴ A+B+C will complete the work in 10 days.

৩৮.
Last year, Company Y earned p dollars in total profit. One-third of the profit was kept for reinvestment, and the remaining amount was divided equally among the company's 6 shareholders. In terms of p, how much did each shareholder receive?
  1. ক
    p/8
  2. খ
    2p/5
  3. গ
    p/6
  4. ঘ
    p/9
সঠিক উত্তর: ঘ
p/9
উত্তর
সঠিক উত্তর: ঘ
p/9
ঘ
ব্যাখ্যা

Question: Last year, Company Y earned p dollars in total profit. One-third of the profit was kept for reinvestment, and the remaining amount was divided equally among the company's 6 shareholders. In terms of p, how much did each shareholder receive?

Solution:
Here,
Company Y's profit is p dollars.

Amount kept for reinvestment = (1/3 of p)
= p/3

∴ Remaining Profit = p - p/3
= (3p - p)/3 = 2p/3

The remaining amount was divided among 6 shareholders.
∴ Each shareholder receives = (2p/3) ÷ 6
= (2p/3) × (1/6)
= p/9

৩৯.
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 175, how much must C pay as his share of rent?
  1. ক
    Tk. 45
  2. খ
    Tk. 50
  3. গ
    Tk. 55
  4. ঘ
    Tk. 60
সঠিক উত্তর: ক
Tk. 45
উত্তর
সঠিক উত্তর: ক
Tk. 45
ক
ব্যাখ্যা
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 175, how much must C pay as his share of rent?

Solution:
A : B : C = (10 × 7) : (12 × 5) : (15 × 3)
= 70 : 60 : 45
= 14 : 12 : 9

∴ C's rent = 175 × (9/35)
= Tk. 45
৪০.
In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C invests the rest of the capital for the whole time. Out of a profit of Tk 3680, C's share is -
  1. ক
    ক) Tk 2480
  2. খ
    খ) Tk 2880
  3. গ
    গ) Tk 3000
  4. ঘ
    ঘ) Tk 3260
সঠিক উত্তর: খ
খ) Tk 2880
উত্তর
সঠিক উত্তর: খ
খ) Tk 2880
খ
ব্যাখ্যা
Question: In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C invests the rest of the capital for the whole time. Out of a profit of Tk 3680, C's share is -

Solution:
Let A invests Tk x/6 for y/6
A invests Tk x/3 for y/3
C invests= x - (x/6 + x/3) = x/2 for y months

Ratio of their investments = (6/x ​× 6/y​) : (3/x​ × 3 /y​) : (2/x ​× y) 
= 1/36 : 1/9 : 1/2
​= 1 : 4 : 18

∴B′s Share = Tk (3680 × 18/23​) = Tk 2880
৪১.
A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
  1. ক
    50%
  2. খ
    40%
  3. গ
    42%
  4. ঘ
    60%
  5. ঙ
    55%
সঠিক উত্তর: ক
50%
উত্তর
সঠিক উত্তর: ক
50%
ক
ব্যাখ্যা

Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

Solution:
Let the Market Price of the product be MP.
Let the Original Cost Price of the product be CP.

Selling Price (Discounted Price) = 100%of MP - 20%MP = 80% of MP ....... (1)
Profit made by selling at discounted price = 20% of CP ....... (2)

Now,  Profit = Selling Price - Original Cost Price
⇒ 20% of CP = 80% of MP - 100% CP
⇒ MP = 120CP/80 = 3/2 (CP)

Now if Product is sold without any discount, then,
​
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= (3/2)CP - CP
= 1/2 CP
= 50% of CP

৪২.
Three partners, X, Y, and Z, invest Tk. 90000 in a business. X invests Tk. 12000 more than Y, and Y invests Tk. 6000 more than Z. If the total profit is Tk. 45000, how much does X receive?
  1. ক
    Tk. 20000
  2. খ
    Tk. 18000
  3. গ
    Tk. 22000
  4. ঘ
    Tk. 24000
  5. ঙ
    Tk. 21000
সঠিক উত্তর: ক
Tk. 20000
উত্তর
সঠিক উত্তর: ক
Tk. 20000
ক
ব্যাখ্যা

Question: Three partners, X, Y, and Z, invest Tk. 90000 in a business. X invests Tk. 12000 more than Y, and Y invests Tk. 6000 more than Z. If the total profit is Tk. 45000, how much does X receive?

Solution:
Let Z's investment be Tk. x.
∴ Y's investment = Tk. (x + 6000)
∴ X's investment = Tk. (x + 6000 + 12000) = Tk. (x + 18000)

Since the total investment is Tk. 90000,
∴ X + Y + Z = 90000
⇒ (x + 18000) + (x + 6000) + x = 90000
⇒ 3x + 24000 = 90000
⇒ 3x = 90000 - 24000
⇒ 3x = 66000
⇒ x = 22000

So, Z's investment = Tk. 22000
Y's investment = Tk. (22000 + 6000) = Tk. 28000
X's investment = Tk. (28000 + 12000) = Tk. 40000

Total profit = Tk. 45000
∴ X's share of profit = (X's investment/Total investment) × Total profit
= (40000/90000) × 45000
= Tk. 20000

∴ X receives Tk. 20000

৪৩.
The banker’s discount on a certain sum due 2 years hence is 11/10 of the true discount. The rate percent is
  1. ক
    ক) 11%
  2. খ
    খ) 10%
  3. গ
    গ) 5%
  4. ঘ
    ঘ) 5.5%
সঠিক উত্তর: গ
গ) 5%
উত্তর
সঠিক উত্তর: গ
গ) 5%
গ
ব্যাখ্যা

Let
True Discount be Tk.1
Then, Banker's Discount = Tk. 11/10 = Tk. 1.10
∴ Sum = Tk {(1.10 × 1)/(1.10 - 1)}
= Tk (110/10)
= Tk. 11
Simple interest on Tk. 11 for 2 years is Tk 1.10
∴ Rate = {(100 × 1.10)/(11 × 2)%
= 5%

৪৪.
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Tk. 6500 for 6 months, B, Tk. 8400 for 5 months and C, Tk. 10000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Tk. 7400. Calculate the share of B in the profit.
  1. ক
    Tk. 2470
  2. খ
    Tk. 1900
  3. গ
    Tk. 2800
  4. ঘ
    Tk. 2660
সঠিক উত্তর: ঘ
Tk. 2660
উত্তর
সঠিক উত্তর: ঘ
Tk. 2660
ঘ
ব্যাখ্যা
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Tk. 6500 for 6 months, B, Tk. 8400 for 5 months and C, Tk. 10000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Tk. 7400. Calculate the share of B in the profit.

Solution:
Ratio of their investments = (6500 × 6) : (8400 × 5) : (10000 × 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10

Sum of the ratio = (13 + 14 + 10) = 37

Here,
The profit earned was Tk. 7400

For working, A received = 5% of Tk. 7400
= Tk. (5 × 7400)/100
= Tk. 370

Remaining profit = Tk. (7400 - 370)
= Tk. 7030

∴ B's share = Tk. {7030 × (14/37)}
= Tk. 2660
৪৫.
Rahim, Sohel and Tarek invested Tk.12000, Tk.9000 and Tk.15000 respectively in a business. Sohel left after four months. If after nine months, there was a gain of Tk.6975, then what will be the share of Tarek in this gain?
  1. ক
    2900 Taka
  2. খ
    3375 Taka
  3. গ
    3100 Taka
  4. ঘ
    None
সঠিক উত্তর: খ
3375 Taka
উত্তর
সঠিক উত্তর: খ
3375 Taka
খ
ব্যাখ্যা
Question: Rahim, Sohel and Tarek invested Tk.12000, Tk.9000 and Tk.15000 respectively in a business. Sohel left after four months. If after nine months, there was a gain of Tk.6975, then what will be the share of Tarek in this gain?

Solution:
Rahim : Sohel : Tarek = (12000 × 9) : (9000 × 4) : (15000 × 9)
= 108000 : 36000 : 135000
= 12 : 4 : 15


∴ Tarek's share = {6975 × (15/31)}
= 3375 Taka
৪৬.
X and Y started a business in partnership investing Tk. 30,000 and Tk. 20,000 respectively. After one year, Z joined them with Tk. 25,000. What will be Y's share in the total profit of Tk. 36,000 earned at the end of 3 years from the starting of the business?
  1. ক
    9000 tk
  2. খ
    9600 tk
  3. গ
    10800 tk
  4. ঘ
    12400 tk
  5. ঙ
    12600 tk
সঠিক উত্তর: গ
10800 tk
উত্তর
সঠিক উত্তর: গ
10800 tk
গ
ব্যাখ্যা
Question: X and Y started a business in partnership investing Tk. 30,000 and Tk. 20,000 respectively. After one year, Z joined them with Tk. 25,000. What will be Y's share in the total profit of Tk. 36,000 earned at the end of 3 years from the starting of the business?

Solution:
X : Y : Z
= (30,000 × 3) : (20,000 × 3) : (25,000 × 2)
= 9 : 6 : 5

So Y's Share = 36,000 × (6/20)
= 10800 tk
৪৭.
Two friends Hasan and Ali started a business with an initial capital contribution of Tk. 50,000 and Tk. 1,00,000. At the end of the year, the business made a profit of Tk. 15,000. Find the share of Hasan in the profit.
  1. ক
    Tk. 7,050
  2. খ
    Tk. 6,500
  3. গ
    Tk. 5,000
  4. ঘ
    Tk. 4,500
সঠিক উত্তর: গ
Tk. 5,000
উত্তর
সঠিক উত্তর: গ
Tk. 5,000
গ
ব্যাখ্যা
Question: Two friends Hasan and Ali started a business with an initial capital contribution of Tk. 50,000 and Tk. 1,00,000. At the end of the year, the business made a profit of Tk. 15,000. Find the share of Hasan in the profit.

Solution:
We know
if the time period of investment is the same, profit or loss is divided by the ratio of the value of the investment.

Here,
Ratio of value of investment of Hasan and Ali = 50,000 : 1,00,000 = 1 : 2
∴ Ratio of share in profit = 1 : 2

∴ the share of Hasan in profit = (1/3) × 15,000 = Tk. 5,000
৪৮.
A, B, C subscribe TK. 50,000 for a business. A subscribes TK. 4,000 more than B and B Tk. 5,000 more than C. Out of a total profit of Tk. 35,000. A receives -
  1. ক
    ক) Tk. 14,700
  2. খ
    খ) Tk. 1,900
  3. গ
    গ) Tk. 13,600
  4. ঘ
    ঘ) TK. 8400
সঠিক উত্তর: ক
ক) Tk. 14,700
উত্তর
সঠিক উত্তর: ক
ক) Tk. 14,700
ক
ব্যাখ্যা

ধরি, C বিনিয়োগ করেছিল x টাকা, B বিনিয়োগ করেছিল (x + 5,000) টাকা
A বিনিয়োগ করেছিল (x + 5,000 + 4,000) = (x + 9,000) টাকা
প্রশ্নমতে, x + x + 5,000 + x + 9,000 = 50,000
⇒ 3x + 14,000 = 50,000
⇒ 3x = 50,000 - 14,000
⇒ 3x = 36,000
⇒ x = 12000 টাকা
অতএব, A, B, C এর বিনিয়োগের অনুপাত
= (12,000 + 9,000) : (12,000 + 5,000) : 12,000
21,000 : 17,000 : 12,000
21 : 17 : 12
∴ A এর মুনাফা = 35000 × (21/50)
= 14,700 টাকা।

৪৯.
A started a business with Tk 24000 and was joined afterward by B with Tk 36000. After how many months did B join if the profits at end of the year are divided equally?
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 5
  4. ঘ
    ঘ) 6
সঠিক উত্তর: খ
খ) 4
উত্তর
সঠিক উত্তর: খ
খ) 4
খ
ব্যাখ্যা
Question: A started a business with Tk 24000 and was joined afterward by B with Tk 36000. After how many months did B join if the profits at end of the year are divided equally?

Solution:
Suppose, B invested after x months

ATQ,
24000 × 12 = 36000 × (12 - x)
⇒ 24 × 12 = 36 × (12 - x)
⇒ 12 - x = (24 × 12)/36
⇒ 12 - x = 8
⇒ x = 4
৫০.
The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?
  1. ক
    18
  2. খ
    19
  3. গ
    20
  4. ঘ
    21
সঠিক উত্তর: ক
18
উত্তর
সঠিক উত্তর: ক
18
ক
ব্যাখ্যা
Question: The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?

Solution:
PW = Tk. 1800
TD = Tk. 180

PW (present worth) = FV (face value) - TD (true discount)
⇒ Face value = present worth + true discount
= 1800 + 180
= 1980

True discount is the simple interest on the present value for the unexpired time.
Now, simple interest on Tk. 1800 for unexpired time = Tk. 180
The rate of simple interest = (180/1800) × 100% = 10%

Banker's discount is the simple interest on the face value of the bill for unexpired time.
simple interest on Tk. 1980 for unexpired time or remaining time.
R = 10%
Banker's discount = 1980 × (10/100) = 198

Banker's gain = Banker's discount - True discount
= 198 - 180
= 18

Alternative Solution:
Banker's gain = (True discount)2/Present worth
= (180)2/1800
= 18
৫১.
A sum of Tk. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is?
  1. ক
    48
  2. খ
    77
  3. গ
    84
  4. ঘ
    98
সঠিক উত্তর: গ
84
উত্তর
সঠিক উত্তর: গ
84
গ
ব্যাখ্যা
Question: A sum of Tk. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is?

Solution:
Given total sum = Tk. 427
And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.
Or, 3A = 4B = 7C

But given,
A + B + C = 427

Now, expressing A and B in terms of C,
(7C/3) + (7C/4) + C = 427
∴ C = 84
৫২.
A, B, C subscribe Tk. 50000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35000. B receives -
  1. ক
    ক) Tk. 11900
  2. খ
    খ) Tk. 14700
  3. গ
    গ) Tk. 10900
  4. ঘ
    ঘ) Tk. 8400
সঠিক উত্তর: ক
ক) Tk. 11900
উত্তর
সঠিক উত্তর: ক
ক) Tk. 11900
ক
ব্যাখ্যা
Question: A, B, C subscribe Tk. 50000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35000. B receives -

Solution:
ধরি,
C বিনিয়োগ করেছিল x টাকা,
B বিনিয়োগ করেছিল (x + 5000) টাকা
A বিনিয়োগ করেছিল (x + 5000 + 4000) = (x + 9000) টাকা

প্রশ্নমতে,
x + x + 5000 + x + 9000 = 50,000
⇒ 3x + 14000 = 50000
⇒ 3x = 50000 - 14000
⇒ 3x = 36000
∴ x = 12000 টাকা

A, B, C এর বিনিয়োগের অনুপাত
= (12000 + 9000) : (12000 + 5000) : 12000
= 21000 : 17000 : 12000
= 21 : 17 : 12

∴ B এর মুনাফা = 35000 × (17/50)
= 11900 টাকা।
৫৩.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
  1. ক
    Tk.375
  2. খ
    Tk. 400
  3. গ
    Tk. 600
  4. ঘ
    Tk. 800
  5. ঙ
    Tk. 1000
সঠিক উত্তর: খ
Tk. 400
উত্তর
সঠিক উত্তর: খ
Tk. 400
খ
ব্যাখ্যা

C's 1 day's work = 1/3 - (1/6 + 1/8)
= 1/3 - 7/24
= 1/24
C's share (for 3 days) = (3 × (1/24) × 3200)
= 400

৫৪.
A, S and D Started a business with the investment of TK 5000, TK 4000 and TK 3000 respectively. At the end of the year, the profit received by S and D together is TK 2000 more than  the profit received by A. What is the total profit of the business?
  1. ক
    12000 TK
  2. খ
    15000 TK
  3. গ
    14000 TK
  4. ঘ
    13000 TK
সঠিক উত্তর: ক
12000 TK
উত্তর
সঠিক উত্তর: ক
12000 TK
ক
ব্যাখ্যা

Question: A, S and D Started a business with the investment of TK 5000, TK 4000 and TK 3000 respectively. At the end of the year, the profit received by S and D together is TK 2000 more than  the profit received by A. What is the total profit of the business?

Solution:

বিনিয়োগের অনুপাত, A : S : D = 5000 : 4000 : 3000
= 5 : 4 : 3

মনে করি,
মোট লাভ p টাকা
∴ A এর লাভ = 5p/12

S এবং D এর লাভ একত্রে = (4P/12) + (3P/12) = 7p/12

প্রশ্নমতে,
7p/12 = (5p/12) + 2000
or, (7p/12 ) - (5p/12) = 2000
or, (7p - 5p)/12 = 2000
or, 2p/12 = 2000
∴ p = 12000

মোট লাভ 12000 টাকা 

৫৫.
Tina and Nila entered into a partnersship with their capitals in the ratio 5 : 6. At the end of 8 months, Tina withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Nila's capital was used?
  1. ক
    ক) 12 months
  2. খ
    খ) 10 months
  3. গ
    গ) 8 months
  4. ঘ
    ঘ) 6 months
সঠিক উত্তর: ক
ক) 12 months
উত্তর
সঠিক উত্তর: ক
ক) 12 months
ক
ব্যাখ্যা
Question: Tina and Nila entered into a partnersship with their capitals in the ratio 5 : 6. At the end of 8 months, Tina withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Nila's capital was used?

Solution: 
Let
The capitals of Nila was used for x months
According to the question,
(5 × 8) : (6 × x) = 5 : 9
(5 × 8)/(6 × x) = 5/9
40/6x = 5/9
30x = 360
x = 360/30
x = 12

Hence capital of Nila was used for = 12 months
৫৬.
Masud and Akram invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Masud invested Tk. 80000, then what was the amount invested by Akram?
  1. ক
    Tk. 150000
  2. খ
    Tk. 70000
  3. গ
    Tk. 120000
  4. ঘ
    Tk. 80000
সঠিক উত্তর: গ
Tk. 120000
উত্তর
সঠিক উত্তর: গ
Tk. 120000
গ
ব্যাখ্যা
Question: Masud and Akram invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Masud invested Tk. 80000, then what was the amount invested by Akram?

Solution:
Given ratio = 2 : 3
Let,
Masud invested 2x Taka
Akram invested 3x Taka

ATQ,
2x = 80000
∴ x = 40000

∴ Akram invested 3x Taka = 3 × 40000 Taka
= 120000 Taka
৫৭.
A company pays rent of Tk. 20000 per month for office space to its owner. But if the company pays the annual rent at the beginning of the year the owner gives a discount of 5% on the total annual rent. What is the annual amount the company pays to the owner after the discount?
  1. ক
    ক) Tk. 226000
  2. খ
    খ) Tk. 225000
  3. গ
    গ) Tk. 228000
  4. ঘ
    ঘ) Tk. 227000
সঠিক উত্তর: গ
গ) Tk. 228000
উত্তর
সঠিক উত্তর: গ
গ) Tk. 228000
গ
ব্যাখ্যা
Question: A company pays rent of Tk. 20000 per month for office space to its owner. But if the company pays the annual rent at the beginning of the year the owner gives a discount of 5% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

Solution:
Total annual rent = Tk. (20000 × 12) = Tk. 240000
Discount = 5% of tk. 240000
= Tk. 12000
∴ Annual rent paid after discount = Tk. (240000 - 12000)
= Tk. 228000
৫৮.
A man distributes Tk. 16,000 among his daughter, wife, and son such that the daughter’s and wife’s shares are in the ratio 1 : 2, and the son receives half of the total amount. What is the daughter’s share? 
  1. ক
    2066.66 Tk
  2. খ
    1666.66 Tk
  3. গ
    2666.66 Tk
  4. ঘ
    2000.66 Tk
সঠিক উত্তর: গ
2666.66 Tk
উত্তর
সঠিক উত্তর: গ
2666.66 Tk
গ
ব্যাখ্যা

Question: A man distributes Tk. 16,000 among his daughter, wife, and son such that the daughter’s and wife’s shares are in the ratio 1 : 2, and the son receives half of the total amount. What is the daughter’s share?

Solution:
The daughter's share and the wife's share are of 1 : 2 ratio
daughter's share = x
wife's share = 2x

As the son gets half of the total amount
∴ son's share = 16000/2
= 8000 Tk

∴ Rest of the share = 3x
∴ According to the question,
Or, 3x = 8000
Or, x = 8000/3
∴ x = 2666.66

∴ daughter's share = x = 2666.66 Tk

৫৯.
A, B and C started a business by investing Tk. 250000, Tk. 300000 and Tk. 350000 respectively. Find the share of B, out of an annual profit of Tk. 187200.
  1. ক
    Tk. 65400
  2. খ
    Tk. 62400
  3. গ
    Tk. 63400
  4. ঘ
    Tk. 66200
সঠিক উত্তর: খ
Tk. 62400
উত্তর
সঠিক উত্তর: খ
Tk. 62400
খ
ব্যাখ্যা
Question: A, B and C started a business by investing Tk. 250000, Tk. 300000 and Tk. 350000 respectively. Find the share of B, out of an annual profit of Tk. 187200.

Solution:
Ratio of shares of A, B and C = Ratio of their investment
A : B : C = 250000 : 300000 : 350000
= 5 : 6 : 7

Share of B = Tk. [(187200 × 6)/ 18] = 62400.
৬০.
A starts business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided between A and B in the ratio 2 : 3. What is B's contribution, in Tk. in the capital? 
  1. ক
    9000
  2. খ
    8500
  3. গ
    8000
  4. ঘ
    7500
  5. ঙ
    None
সঠিক উত্তর: ক
9000
উত্তর
সঠিক উত্তর: ক
9000
ক
ব্যাখ্যা
Question: A starts business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided between A and B in the ratio 2 : 3. What is B's contribution, in Tk. in the capital?

Solution:
Let B's capital be Tk. x.
Then,
(3500 × 12)/7x = 2/3
⇒ 14x = 126000
∴ x = 9000.
৬১.
A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk.  4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 30,000, A receives
  1. ক
    ক) Tk. 10800
  2. খ
    খ) Tk. 7200
  3. গ
    গ) Tk. 10200
  4. ঘ
    ঘ) Tk. 12600
সঠিক উত্তর: ঘ
ঘ) Tk. 12600
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. 12600
ঘ
ব্যাখ্যা
Question: A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk.  4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 30,000, A receives

Solution: 
Let
C = x.
B = x + 5000
A = x + 5000 + 4000 = x + 9000
Now 
So, x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000
A : B : C = 21000 : 17000 : 12000
              = 21 : 17 : 12

So A's Share = Tk. 30000 × (21/50) =Tk. 12600
৬২.
An item is sold at 25% discount making a profit of 20%. If the discount is reduced to 15%, what will be the new profit percentage?
  1. ক
    32%
  2. খ
    46%
  3. গ
    24%
  4. ঘ
    36%
সঠিক উত্তর: ঘ
36%
উত্তর
সঠিক উত্তর: ঘ
36%
ঘ
ব্যাখ্যা
Question: An item is sold at 25% discount making a profit of 20%. If the discount is reduced to 15%, what will be the new profit percentage?

Solution:
Let,
the cost price is 100
So, the selling price is 120

Giving 25% discount, then
⇒ x - 25% of x = 120
⇒ x - (x/4) = 120
⇒ 3x/4 = 120
∴ x = 160 

Now,
giving 15% discount,
160 - 15% of 160 = 160 - 24 = 136
So the new selling price is 136 taka.

So profit = 136 - 100 = 36

When the discount is reduced to 15%, the profit becomes 36%.
৬৩.
Mannan and Hannan rent a pasture for 12 months. Mannan puts in 200 cows for 8 months. How many cows can Hannan put in the pasture for the remaining 4 months if he pays 1.5 as much as Mannan?
  1. ক
    450 cows
  2. খ
    600 cows
  3. গ
    300 cows
  4. ঘ
    520 cows
সঠিক উত্তর: খ
600 cows
উত্তর
সঠিক উত্তর: খ
600 cows
খ
ব্যাখ্যা
Question: Mannan and Hannan rent a pasture for 12 months. Mannan puts in 200 cows for 8 months. How many cows can Hannan put in the pasture for the remaining 4 months if he pays 1.5 as much as Mannan?

Solution:
Let Mannan's cow (C1) = 200 cows, and time spend T1 = 8 months
Hannan's cow (C2) = y cows, and time spend T2 = 4 months
Let the profit of Mannan = x
Then the profit of Hannan =  1.5x = (3/2)x = (3x/2)

(C1 × T1)/ (C2 × T2) = p1/p2
⇒ (200 × 8)/ (y × 4) = x/ (3x/2)
⇒ 400/y = 2x/3x
⇒ 400/y = 2/3
⇒ y = (400 × 3)/2
∴ y = 600

Hence, Hannan can put 600 cows for the remaining 4 months.
৬৪.
P and Q started a business in the ratio of 2 : 3. After, 1 year P left the business but Q continued. After 2 years they had the profit of Tk. 26,000. What is the profit of Q? 
  1. ক
    Tk. 5000.
  2. খ
    Tk. 20500.
  3. গ
    Tk. 19500.
  4. ঘ
    Tk. 10500.
সঠিক উত্তর: গ
Tk. 19500.
উত্তর
সঠিক উত্তর: গ
Tk. 19500.
গ
ব্যাখ্যা

Question: P and Q started a business in the ratio of 2 : 3. After, 1 year P left the business but Q continued. After 2 years they had the profit of Tk. 26,000. What is the profit of Q?

Solution:
Let the initial capital of P and Q be 2x and 3x, respectively.

Then, ratio of profits
= 2x × 12 : 3x × 24
= 24x : 72x
= 1 : 3

∴ Q's share of profit
= 26000 × (3/4)
= Tk. 19500.

৬৫.
Tofail, Hasib, Hemal enter into a partnership. Tofail initially invests 25 lakh & adds another 10 lakhs after one year. Hasib initially invests 35 lakh & withdrawal 10 lakh after 2 years and Hemal invests 30 Lakh. In what ratio should the profit be divided at the end of 3 years?
  1. ক
    ক) 19 : 19 : 18
  2. খ
    খ) 17 : 18 : 19
  3. গ
    গ) 18 : 18 : 19
  4. ঘ
    ঘ) 17 : 17: 19
সঠিক উত্তর: ক
ক) 19 : 19 : 18
উত্তর
সঠিক উত্তর: ক
ক) 19 : 19 : 18
ক
ব্যাখ্যা
প্রশ্ন: Tofail, Hasib, Hemal enter into a partnership. Tofail initially invests 25 lakh & adds another 10 lakhs after one year. Hasib initially invests 35 lakh & withdrawal 10 lakh after 2 years and Hemal invests 30 Lakh. In what ratio should the profit be divided at the end of 3 years?

সমাধান: 
Tofail : Hasib : Hemal = (25 × 1 + 35 × 2) : (35 × 2 + 25 × 1) : (30 × 3)
= (25 + 70) : (70 + 25) : 90
= 95 : 95 : 90
= 19 : 19: 18 
৬৬.
P, Q, R have the total money of Tk. 2800. Q have half of P and R have half of Q. The amount of R is
  1. ক
    ক) 400 Tk.
  2. খ
    খ) 600 Tk.
  3. গ
    গ) 800 Tk.
  4. ঘ
    ঘ) 1600 Tk.
সঠিক উত্তর: ক
ক) 400 Tk.
উত্তর
সঠিক উত্তর: ক
ক) 400 Tk.
ক
ব্যাখ্যা
question: P, Q, R have the total money of Tk. 2800. Q have half of P and R have half of Q. The amount of R is 

Solution: 
Let P have x

then, 
Q have x/2 and
R have x/4


Now
x + (x/2) + (x/4) = 2800
7x/4 = 2800
x = 1600

Hence, 
The amount of R is (1600/4) = 400
৬৭.
The marked price of a Footwear is Tk. 200, and it is sold after applying two successive 20% discounts. What is the final price at which it is sold? 
  1. ক
    Tk. 500
  2. খ
    Tk. 600
  3. গ
    Tk. 900
  4. ঘ
    Tk. 128
  5. ঙ
    None
সঠিক উত্তর: ঘ
Tk. 128
উত্তর
সঠিক উত্তর: ঘ
Tk. 128
ঘ
ব্যাখ্যা

Question: The marked price of a Footwear is Tk. 200, and it is sold after applying two successive 20% discounts. What is the final price at which it is sold?

Solution:
Discount 1 = 200 × (20/100) = Tk. 40

Selling price after 1st discount = 200 - 40 = Tk. 160

Discount 2 = 160 × (20/100) = Tk. 32

∴ Selling price after 2nd discount = 160 - 32 = Tk. 128

৬৮.
Sayed started a software business by investing Tk. 20000. After six months, Rafi joined him with a capital of Tk. 30000. After 3 years, they earned a profit of Tk. 13950. What was Sayed’s share in the profit?
  1. ক
    Tk. 6200
  2. খ
    Tk. 6400
  3. গ
    Tk. 4200
  4. ঘ
    Tk. 7750
সঠিক উত্তর: ক
Tk. 6200
উত্তর
সঠিক উত্তর: ক
Tk. 6200
ক
ব্যাখ্যা
Question: Sayed started a software business by investing Tk. 20000. After six months, Rafi joined him with a capital of Tk. 30000. After 3 years, they earned a profit of Tk. 13950. What was Sayed’s share in the profit?

Solution:
Ratio of capitals of Sayed and Rafi
= (20000 × 36) : (30000 × 30)
= 720000 : 900000
= 4 : 5.

Sayed’s share is = Tk. (13950 × 4)/9 = Tk. 6200.
৬৯.
A man purchased a shirt at Tk. 450 after availing a discount of 25%. What is the catalog price of the shirt?
  1. ক
    Tk. 490
  2. খ
    Tk. 530
  3. গ
    Tk. 560
  4. ঘ
    Tk. 590
  5. ঙ
    Tk. 600
সঠিক উত্তর: ঙ
Tk. 600
উত্তর
সঠিক উত্তর: ঙ
Tk. 600
ঙ
ব্যাখ্যা
Question: A man purchased a shirt at Tk. 450 after availing a discount of 25%. What is the catalog price of the shirt?

Solution: 
25% discount,
If the catalog price is Tk. 100 then the purchased = (100 - 25)
= Tk. 75

If the purchase price is Tk. 75, the catalog price = 100 taka.
If the purchase price is Tk. 1, the catalog price = 100/75 taka
If the purchase price is Tk. 450, the catalog price = (100 × 450)/75 taka
= Tk. 600
৭০.
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Tk. 6500 for 6 months, B, Tk. 8400 for 5 months and C, Tk. 10,000 for 3 months. B wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Tk. 7400. Calculate the share of C in the profit.
  1. ক
    Tk. 1680
  2. খ
    Tk. 1900
  3. গ
    Tk. 2470
  4. ঘ
    Tk. 2660
  5. ঙ
    None 
সঠিক উত্তর: খ
Tk. 1900
উত্তর
সঠিক উত্তর: খ
Tk. 1900
খ
ব্যাখ্যা

Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Tk. 6500 for 6 months, B, Tk. 8400 for 5 months and C, Tk. 10,000 for 3 months. B wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Tk. 7400. Calculate the share of C in the profit.

Solution:

For managing, B received = 5% of Tk. 7400
= (5/100) × 7400
= Tk. 370

Balance = Tk. (7400 - 370)
= Tk. 7030

∴ Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

= 39000 : 42000 : 30000

= 13 : 14 : 10

Sum of the ratio = (13 + 14 + 10) = 37

C's share = [7030 × (10/37)]
= Tk. 1900  

৭১.
A, B and C are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). A withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of C is -
  1. ক
    Tk. 1240
  2. খ
    Tk. 1250
  3. গ
    Tk. 1300
  4. ঘ
    Tk. 1400
সঠিক উত্তর: ক
Tk. 1240
উত্তর
সঠিক উত্তর: ক
Tk. 1240
ক
ব্যাখ্যা
Question:  A, B and C are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). A withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of C is -

Solution: 
Ratio of initial investments = 1/3 : 1/4 : 1/5
= 20 : 15 : 12

Let their initial investments be 20x, 15x and 12x respectively.

A : B : C = (20x × 15) + (10x × 15): (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4

Sum of the ratio = 5 + 5 + 4 = 14.

C's share = 4340 × (4/14)
= 1240 Tk.
৭২.
After successive discount of 12% and 5% an article was sold for Tk.209. What was the original price of the article?
  1. ক
    ক) Tk. 220
  2. খ
    খ) Tk. 250
  3. গ
    গ) Tk. 260
  4. ঘ
    ঘ) Tk. 280
সঠিক উত্তর: খ
খ) Tk. 250
উত্তর
সঠিক উত্তর: খ
খ) Tk. 250
খ
ব্যাখ্যা
Let the original price x 
Now
95% of 88% of x = 209 
(95/100) × (88/100)  × x = 209 
x = (209 × 100 × 100)/(95 × 88)
x = 250
৭৩.
A and B start a business jointly. A invests Tk 16000 for 8 months and B remains in the business for 4 months. Out of the total profit, B claims 2/7 of the profit. How much money was contributed by B?
  1. ক
    ক) 10000 Tk
  2. খ
    খ) 11200 Tk
  3. গ
    গ) 12000 Tk
  4. ঘ
    ঘ) 12800 Tk
সঠিক উত্তর: ঘ
ঘ) 12800 Tk
উত্তর
সঠিক উত্তর: ঘ
ঘ) 12800 Tk
ঘ
ব্যাখ্যা
Question: A and B start a business jointly. A invests Tk 16000 for 8 months and B remains in the business for 4 months. Out of the total profit, B claims 2/7 of the profit. How much money was contributed by B?

Solution:
Here,
Total profit = 7
B's profit = 2
So, A's profit = 7 - 2 = 5

So, ratio of A's and B's profit = 5 : 2

Let B's capital be x
Then,
(16000 × 8)/(x × 4) = 5/2
⇒ 20x = 16000 × 8 × 2
⇒ x = (16000 × 8 × 2)/20
⇒ 12800
৭৪.
A trader marks his goods at 40% above the cost price but allows a discount of 20% on the marked price. His profit percentage is-
  1. ক
    8% 
  2. খ
    10% 
  3. গ
    12% 
  4. ঘ
    15%
সঠিক উত্তর: গ
12% 
উত্তর
সঠিক উত্তর: গ
12% 
গ
ব্যাখ্যা

Question: A trader marks his goods at 40% above the cost price but allows a discount of 20% on the marked price. His profit percentage is-
 
Solution: 
Let
the Cost Price of the goods Tk.100

∴ Marked price of the goods  = 100 + 40% of 100
= 100 + (40 × 100)/100
= 100 + 40 
 = 140

∴ Selling Price of the goods = 80% of 140
= (140 × 80)/100
= 112

∴ profit = 112 - 100 = 12 Tk.

∴ profit percentage is = (12/100) × 100%
= 12%

৭৫.
Monir and Mohin bought the same item. Monir paid Tk 15,000. Mohin got discount and paid Tk. 3,000 less than Monir. How much discount did Mohin get?
  1. ক
    10%
  2. খ
    15%
  3. গ
    18%
  4. ঘ
    20%
সঠিক উত্তর: ঘ
20%
উত্তর
সঠিক উত্তর: ঘ
20%
ঘ
ব্যাখ্যা
Question: Monir and Mohin bought the same item. Monir paid Tk 15,000. Mohin got discount and paid Tk. 3,000 less than Monir. How much discount did Mohin get?

Solution:
In Tk. 15000 Mohin get discount Tk. 3000
In Tk. 1 Mohin get discount Tk. (3000/15000)
In Tk. 100 Mohin get discount Tk. (3000 × 100)/15000
= Tk. 20

∴ Mohin get 20% discount.
৭৬.
A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio -
  1. ক
    ক) 17 : 14
  2. খ
    খ) 19 : 16
  3. গ
    গ) 16 : 15
  4. ঘ
    ঘ) 18 : 15
সঠিক উত্তর: গ
গ) 16 : 15
উত্তর
সঠিক উত্তর: গ
গ) 16 : 15
গ
ব্যাখ্যা
For an income of Tk. 1 in 9% stock at 96,
investment = Tk. (96/9)
= Tk. 32/3

For an income of Tk. 1 in 12% stock at 120,
investment = Tk. (120/12)
= Tk. 10

Ratio of investments = (32/3) : 10
= 32 : 30
= 16 : 15.
৭৭.
After successive discount of 12% and 5% an article was sold for Tk.209. What was the original price of the article?
  1. ক
    ক) Tk. 260
  2. খ
    খ) Tk. 270
  3. গ
    গ) Tk. 280
  4. ঘ
    ঘ) Tk. 250
সঠিক উত্তর: ঘ
ঘ) Tk. 250
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. 250
ঘ
ব্যাখ্যা
Question: After successive discount of 12% and 5% an article was sold for Tk.209. What was the original price of the article?

Solution: 
Let the original price x 
Now
95% of 88% of x = 209 
(95/100) × (88/100)  × x = 209 
x = (209 × 100 × 100)/(95 × 88)
x = 250
৭৮.
A and B invested in the ratio of 11 : 12. B invested for 11 month. If the profit ratio of A and B is 2 : 3, for how much time A invested the money?
  1. ক
    ক) 8 month
  2. খ
    খ) 12 month
  3. গ
    গ) 10 month
  4. ঘ
    ঘ) 9 month
সঠিক উত্তর: ক
ক) 8 month
উত্তর
সঠিক উত্তর: ক
ক) 8 month
ক
ব্যাখ্যা
Question: A and B invested in the ratio of 11 : 12. B invested for 11 month. If the profit ratio of A and B is 2 : 3, for how much time A invested the money?

Solution: 
Let A and B invested 11p and 12p, 
A invested for Y month

Then,
(11p × Y) : (12p × 11) = 2 : 3
11Y : 132 = 2 : 3
33Y = 264
Y = 8
৭৯.
A and B are business partners. A invests Tk. 20,000 for 4 months, while B invests Tk. 30,000 for 6 months. If the total profit at the end of the year is Tk. 65,000, what is B’s share of the profit?
  1. ক
    45000 Taka
  2. খ
    52000 Taka
  3. গ
    62000 Taka
  4. ঘ
    20000 Taka
সঠিক উত্তর: ক
45000 Taka
উত্তর
সঠিক উত্তর: ক
45000 Taka
ক
ব্যাখ্যা

Question: A and B are business partners. A invests Tk. 20,000 for 4 months, while B invests Tk. 30,000 for 6 months. If the total profit at the end of the year is Tk. 65,000, what is B’s share of the profit?

Solution: 
A’s Contribution = 20000 × 4 = 80000 Taka
B’s Contribution = 30000 × 6 = 180000 Taka

The ratio of A's and B's investment = 80000 : 180000
= 4 : 9

So, B's share in profit = {9/(4+9)} × 65000
= 45000 Taka

৮০.
A store runs a "Buy 3, Get 1 Free" offer. What is the equivalent discount percentage?
  1. ক
    20%
  2. খ
    25%
  3. গ
    30%
  4. ঘ
    16%
সঠিক উত্তর: খ
25%
উত্তর
সঠিক উত্তর: খ
25%
খ
ব্যাখ্যা
Question: A store runs a "Buy 3, Get 1 Free" offer. What is the equivalent discount percentage?

Solution:
Assume the price of each item = 1 Taka.
Then,
Cost of 3 items = 3 Taka
Since 1 item is received for free, total items = 3 + 1 = 4

After the discount,
Cost of 4 items = 3 Taka
∴ Cost per item = 3/4 Taka

Actual price per item = 1 Taka
∴ Discount per item = 1 − ( 3/4 ) = 1/4 Taka

So, discount on 1 Taka = 1/4 Taka
∴ Discount on 100 Taka = 100 × ( 1/4 ) = 25 Taka

Therefore, in a “Buy 3, Get 1 Free” offer, the equivalent discount is 25%.
৮১.
The price of a t-shirt is Tk. 50. If you buy more than 3 shirts, you will get 12% discount. How much do you have to pay if you buy 8 shirts?
  1. ক
    Tk. 370
  2. খ
    Tk. 350
  3. গ
    Tk. 352
  4. ঘ
    Tk. 358
সঠিক উত্তর: গ
Tk. 352
উত্তর
সঠিক উত্তর: গ
Tk. 352
গ
ব্যাখ্যা
Question: The price of a t-shirt is Tk. 50. If you buy more than 3 shirts, you will get 12% discount. How much do you have to pay if you buy 8 shirts?

Solution:
The price of 1 t-shirt 50
∴ The price of 8 t-shirt (50 × 8) 
= 400

If price 100 then have to be paid 88
If price 1 then have to be paid 88/100
If price 400 then have to be paid (88 × 400)/100
= 352
৮২.
An umbrella marked at Tk. 80 is sold for Tk. 68. The rate of discount is:
  1. ক
    ক) 15%
  2. খ
    খ) 12%
  3. গ
    গ) 17.5%
  4. ঘ
    ঘ) 20%
  5. ঙ
    ঙ) 25%
সঠিক উত্তর: ক
ক) 15%
উত্তর
সঠিক উত্তর: ক
ক) 15%
ক
ব্যাখ্যা

Discount = 80 - 68 = 12
Discount Rate = (12/80) × 100
= 15%

৮৩.
X, Y, and Z started a business by investing Tk. 150000, Tk. 250000 and Tk. 100,000 respectively. Find the share of Y, out of an annual profit of Tk. 100,000.
  1. ক
    Tk. 30000
  2. খ
    Tk. 40000
  3. গ
    Tk. 50000
  4. ঘ
    Tk. 60000
সঠিক উত্তর: গ
Tk. 50000
উত্তর
সঠিক উত্তর: গ
Tk. 50000
গ
ব্যাখ্যা
Question: X, Y, and Z started a business by investing Tk. 150000, Tk. 250000 and Tk. 100,000 respectively. Find the share of Y, out of an annual profit of Tk. 100,000.

Solution:
Ratio of shares of A, B and C = Ratio of their investment
X : Y : Z = 150000 : 250000 : 100000
= 3 : 5 : 2

∴ Total parts = 3 + 5 + 2 = 10

∴ Share of Y = Tk. [(100000 × 5)/ 10] = 50000
৮৪.
Robin invests a part of Tk. 12000 in 12% stock at Tk. 120 and the remainder in 15% stock at Tk. 125. If his total dividend per annum is Tk. 1360, how much does he invest in 12% stock at Tk. 120?
  1. ক
    ক) Tk. 2500
  2. খ
    খ) Tk. 3500
  3. গ
    গ) Tk. 4000
  4. ঘ
    ঘ) Tk. 1500
সঠিক উত্তর: গ
গ) Tk. 4000
উত্তর
সঠিক উত্তর: গ
গ) Tk. 4000
গ
ব্যাখ্যা
Let investment in 12% stock be Tk. x
Investment in 15% stock = 12000 – x

According to the question,
12/120 × x + 15/125 × (12000 – x) = 1360
x/10 + 3/25 (12000 – x) = 1360
5x + 72000 – 6x = 1360 × 50
x = 72,000 - 68,000
x = 4,000
৮৫.
A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price, how much profit or loss does he make, if any?
  1. ক
    1% gain
  2. খ
    1% loss
  3. গ
    5% gain
  4. ঘ
    5% loss
  5. ঙ
    No gain, no loss.
সঠিক উত্তর: খ
1% loss
উত্তর
সঠিক উত্তর: খ
1% loss
খ
ব্যাখ্যা
Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price, how much profit or loss does he make, if any?

Solution:
Let the cost price be Tk. 100.
Marked price = Tk. 110 (10% above CP)
Discount = 10% on the marked price = 10% of 110 = Tk. 11
∴ Selling price = 110 - 11 = Tk. 99
∴ Loss = CP - SP = 100 - 99 = Tk. 1 
∴ % of loss = 1%
৮৬.
Sumon started a business with a capital of Tk. 80000. After 6 months Mohan joined as a partner by investing Tk. 65000. After one year they earned total profit Tk. 20000. What is share of Mohan in the profit?
  1. ক
    Tk. 5222.2
  2. খ
    Tk. 5777.7
  3. গ
    Tk. 6222.2
  4. ঘ
    Tk. 6777.7
সঠিক উত্তর: খ
Tk. 5777.7
উত্তর
সঠিক উত্তর: খ
Tk. 5777.7
খ
ব্যাখ্যা
Question: Sumon started a business with a capital of Tk. 80000. After 6 months Mohan joined as a partner by investing Tk. 65000. After one year they earned total profit Tk. 20000. What is share of Mohan in the profit?

Solution:
Sumon : Mohan = (80000 × 12) : (65000 × 6)
= 960000 : 390000
= 96 : 39
= 32 : 13

∴ Mohan's Share in the profit = (13/45) × 20000
= 5777.77
৮৭.
Tk. 355 has been divided among A, B, C in such a way that A had Tk. 20 more than B and C had Tk.15 more than A. How much was C’s share?
  1. ক
    ক) Tk. 135
  2. খ
    খ) Tk. 100
  3. গ
    গ) Tk. 120
  4. ঘ
    ঘ) Tk. 150
সঠিক উত্তর: ক
ক) Tk. 135
উত্তর
সঠিক উত্তর: ক
ক) Tk. 135
ক
ব্যাখ্যা

Let the share of A was x
A has 20 more than B.
So, Share of B was (x – 20)
And C had 15 more than A So, Share of C was (x + 15)
ATQ,
A + B + C = 355
Or, x + x – 20 + x + 15 = 355
Or, 3x – 5 = 355
Or, 3x = 360
Or, x = 120

So, Share of C = x + 15 = 120 + 15 = 135

৮৮.
X and Y start a business by investing a certain amount in the ratio 9:16. Both of them invest for an equal period of time. At the end of the term, X’s share of profit is what percent less than that of Y?
  1. ক
    ক) 62(1/2)
  2. খ
    খ) 60
  3. গ
    গ) 55(2/3)
  4. ঘ
    ঘ) 43(3/4)
সঠিক উত্তর: ঘ
ঘ) 43(3/4)
উত্তর
সঠিক উত্তর: ঘ
ঘ) 43(3/4)
ঘ
ব্যাখ্যা

Let, X’s investment 9x and Y’s investment 16x
X’s profit less than that of Y is = (16x - 9x)/16x × 100
= (7×100)/16 
= 175/4
= 43(3/4)

৮৯.
Three friends Alice, Bond and Charlie divide $1,105 among them is such a way that if $10, $20 and $15 are removed from the sums that Alice, Bond and Charli received respectively than the share of the sums that they got will be in the ratio of 11 : 18 : 24 . How mush did Charlie receive?
  1. ক
    ক) 495
  2. খ
    খ) 510
  3. গ
    গ) 375
  4. ঘ
    ঘ) 360
সঠিক উত্তর: ক
ক) 495
উত্তর
সঠিক উত্তর: ক
ক) 495
ক
ব্যাখ্যা
Question: Three friends Alice, Bond and Charlie divide $1,105 among them is such a way that if $10, $20 and $15 are removed from the sums that Alice, Bond and Charli received respectively than the share of the sums that they got will be in the ratio of 11 : 18 : 24 . How mush did Charlie receive?

Solution: 
Alice, Bond and Charlie received Tk. 11x, Tk. 18x, and Tk. 24x respectively.
After removing $10, $20 and $15 from the sum 

Now
11x + 18x + 24x = 1105 - (10 + 20 + 15)
53x = 1105 - 45
53x = 1060
x = 1060/53
x = 20 

Charlie received = Tk. 24x +  15)
= Tk.(24 × 20 + 15)
=  Tk.495
৯০.
By selling a book for Tk. 675, a seller loses 2/9 of his outlay, by selling it for Tk. 810, his gain or loss percentage is -
  1. ক
    ক) 6.67% loss
  2. খ
    খ) 6.67% gain
  3. গ
    গ) 7.34% loss
  4. ঘ
    ঘ) 7.34% gain
সঠিক উত্তর: ক
ক) 6.67% loss
উত্তর
সঠিক উত্তর: ক
ক) 6.67% loss
ক
ব্যাখ্যা
A seller loses 2/9 of his outlay,
that means if selling price is Tk. 7, then cost price will be (7 + 2) = Tk. 9
if selling price is Tk. 675, then cost price will be Tk. 9 × 675/7 = Tk. 867.86
Loss = Tk. (867.86 - 810) = Tk. 57.86
percentage loss = Tk. 57.86/Tk. 867.86 × 100% = 6.67%
৯১.
A and B started a business investing amounts in the ratio of 2 : 3. If A has invested an additional amount of Tk. 12000, their ratio of investment would have been 3 : 2. The amount invested by A was?
  1. ক
    Tk. 6500
  2. খ
    Tk. 8000
  3. গ
    Tk. 8500
  4. ঘ
    Tk. 9600
সঠিক উত্তর: ঘ
Tk. 9600
উত্তর
সঠিক উত্তর: ঘ
Tk. 9600
ঘ
ব্যাখ্যা
Question: A and B started a business investing amounts in the ratio of 2 : 3. If A has invested an additional amount of Tk. 12000, their ratio of investment would have been 3 : 2. The amount invested by A was?

Solution:
Let, their respective investments are 2x and 3x

If A added Tk. 12000 to his investment
Then the new ratio = 3 : 2

∴ (2x + 12000) : 3x = 3 : 2
⇒ 9x = 4x + 24000
⇒ 5x = 24000
⇒ x = 4800

Hence, the investment of A is = (2 × 4800)
= 9600
৯২.
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk. 855, the total profit is-
  1. ক
    Tk. 1425
  2. খ
    Tk. 1500
  3. গ
    Tk. 1537.50
  4. ঘ
    Tk. 1576
সঠিক উত্তর: খ
Tk. 1500
উত্তর
সঠিক উত্তর: খ
Tk. 1500
খ
ব্যাখ্যা
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk. 855, the total profit is-

Solution:
Let the total profit be Tk. 100.
After paying to charity,A's share = Tk. 95 × (3/5) = Tk. 57.

If A's share is Tk. 57, total profit = Tk. 100.
If A's share Tk. 855, total profit = (100 × 855)/57 = 1500.
৯৩.
'A' began a business with Tk. 85000. He was joined afterwards by 'B' with Tk. 42500. For how much period does 'B' join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
  1. ক
    4 months
  2. খ
    5 months
  3. গ
    7 months
  4. ঘ
    8 months
সঠিক উত্তর: ঘ
8 months
উত্তর
সঠিক উত্তর: ঘ
8 months
ঘ
ব্যাখ্যা

Question: 'A' began a business with Tk. 85000. He was joined afterwards by 'B' with Tk. 42500. For how much period does 'B' join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

Solution: 
Suppose 'B' joined for x months.

Now,
A's capital = Tk. 85000, time = 12 months
B's capital = Tk. 42500, time = x months

According to the question,
A's share : B's Share = 3 : 1
⇒ (85000 × 12)/(42500 × x) = 3/1
⇒ x = (85000 × 12)/(42500 × 3)
⇒ x = 8
∴ 'B' joined for 8 months.

৯৪.
Find the difference of amount if 40% discount is given on Tk. 500 and two consecutive discounts 30% and 10% are given on the same amount.
  1. ক
    ক) Tk. 10
  2. খ
    খ) Tk. 15
  3. গ
    গ) Tk. 20
  4. ঘ
    ঘ) Tk. 25
সঠিক উত্তর: খ
খ) Tk. 15
উত্তর
সঠিক উত্তর: খ
খ) Tk. 15
খ
ব্যাখ্যা
Question: Find the difference of amount if 40% discount is given on Tk. 500 and two consecutive discounts 30% and 10% are given on the same amount.

Solution:
40% discount on 500 = 500 × 40% = 200

Two consecutive discount on 500.
30% discount on 500 = 500 - 30% of 500
= 500 - 150
= 350

Again,
10% discount on 350 = 350 - 10% of 350
= 350 - 35
= 315

Total discount = 150 + 35 = Tk. 185
So, difference = 200 - 185 = Tk. 15
৯৫.
If A invests Tk 5,000 for 12 months and B invests Tk 6,000 for 10 months, what is the ratio of their profits?
  1. ক
    5 : 6
  2. খ
    1 : 1
  3. গ
    1 : 2
  4. ঘ
    1 : 1.2
সঠিক উত্তর: খ
1 : 1
উত্তর
সঠিক উত্তর: খ
1 : 1
খ
ব্যাখ্যা
Question: If A invests Tk 5,000 for 12 months and B invests Tk 6,000 for 10 months, what is the ratio of their profits?

Solution:
We know, profit = (investment × time)
A has a profit of 5,000 × 12 = 60,000
B has a profit of  6,000 × 10 = 60,000
∴ So ratio of A's profit to B's profit = 60,000 : 60,000 = 1 : 1
৯৬.
The price of a motorbike is 1,50,000. How much do you need to pay if you get a 10% discount?
  1. ক
    Tk. 135000
  2. খ
    Tk. 140000
  3. গ
    Tk. 155000
  4. ঘ
    Tk. 165000
সঠিক উত্তর: ক
Tk. 135000
উত্তর
সঠিক উত্তর: ক
Tk. 135000
ক
ব্যাখ্যা
Question: The price of a motorbike is 1,50,000. How much do you need to pay if you get a 10% discount?

Solution:
For 10% discount,
Original price 100 paid price 90
∴ Original price 1 paid price 90/100
∴ Original price 150000 paid price (90 × 150000)/100
= 135000
৯৭.
The marked price of a ceiling fan is Tk. 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.
  1. ক
    Tk. 1200
  2. খ
    Tk. 1185
  3. গ
    Tk. 1175
  4. ঘ
    Tk. 1150
সঠিক উত্তর: গ
Tk. 1175
উত্তর
সঠিক উত্তর: গ
Tk. 1175
গ
ব্যাখ্যা
Question: The marked price of a ceiling fan is Tk. 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.

Solution:
Marked price = Tk. 1250 and discount = 6%. 

Discount = 6% of Marked Price 
= (6% of Tk. 1250) 
= Tk. {1250 × (6/100)} 
= Tk. 75 

Selling price = (Marked Price) - (discount) 
= Tk. (1250 - 75) 
= Tk. 1175. 

∴ Hence, the selling price of the fan is Tk. 1175. 
৯৮.
A, B and C started a business each investing Tk.10000. After 4 month A withdraws Tk.3000, B withdraws Tk.4000, C invest Tk.3000 more At the end of the years, a total profit was Tk.32800. Find the share of C.
  1. ক
    Tk. 10000
  2. খ
    Tk. 14400
  3. গ
    Tk. 17600
  4. ঘ
    Tk. 19200
সঠিক উত্তর: খ
Tk. 14400
উত্তর
সঠিক উত্তর: খ
Tk. 14400
খ
ব্যাখ্যা
Question: A, B and C started a business each investing Tk. 10000. After 4 month A withdraws Tk. 3000, B withdraws Tk.4000, C invest Tk. 3000 more At the end of the years, a total profit was Tk. 32800. Find the share of C.

Solution:
Ratio of capital of A, B and C.
= (10000 × 4 + 7000 × 8) : (10000 × 4 + 6000 × 8) : (10000 × 4 + 13000 × 8)
= 96000 : 88000 : 144000
= 12 : 11: 18

Distributing the final profit of Tk. 32800 in the given ratio, the share of C becomes = (32800 × 18)/41 = 14400.
৯৯.
A shop offers a discount of 12% on a refrigerator that originally costs Tk. 50000. What is the selling price after the discount?
  1. ক
    Tk. 44000
  2. খ
    Tk. 42500
  3. গ
    Tk. 48000
  4. ঘ
    Tk. 45500
  5. ঙ
    Tk. 40800
সঠিক উত্তর: ক
Tk. 44000
উত্তর
সঠিক উত্তর: ক
Tk. 44000
ক
ব্যাখ্যা
Question: A shop offers a discount of 12% on a refrigerator that originally costs Tk. 50000. What is the selling price after the discount?

Solution:
The original price of the refrigerator = Tk. 50000
And the discount percentage = 12%

We know,
Discount Amount = (Discount Percentage/100​) × Original Price
= (12/100) × 50000
= 6000

∴ Selling Price = 50000 - 6000 = 44000
The selling price after the discount is Tk. 44000.
১০০.
A shirt is being sold for Tk. 720 after a 25% discount. Determine its original price.
  1. ক
    Tk. 900
  2. খ
    Tk. 960
  3. গ
    Tk. 1000
  4. ঘ
    Tk. 1080
সঠিক উত্তর: খ
Tk. 960
উত্তর
সঠিক উত্তর: খ
Tk. 960
খ
ব্যাখ্যা

Question: A shirt is being sold for Tk. 720 after a 25% discount. Determine its original price.

Solution:
Given,
Let the original price be x Tk.

Discount = 25% of x
= 25x/100
= x/4

∴ Selling Price = Original Price - Discount
= x - (x/4)
= 3x/4

Now,
3x/4 = 720
⇒ 3x = 720 × 4
⇒ 3x = 2880
∴ x = 960 

∴ Original price = 960 Tk