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Partnership and Discount

মোট প্রশ্ন৪৪৪এই পাতা১০০প্রতি পাতা১০০
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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Partnership and Discount

PrepBank · পাতা ৪ / ৫ · ৩০১–৪০০ / ৪৪৪

৩০১.
A, B and C enter into partnership with investments in the ratio of 5 : 6 : 9. If, at the end of the year B's share of profit is tk 40,350, how much is the total profit?
  1. ক
    Tk. 134,000
  2. খ
    Tk. 134,500
  3. গ
    Tk. 125,500
  4. ঘ
    Tk. 243,500
ব্যাখ্যা
Question: A, B and C enter into partnership with investments in the ratio of 5 : 6 : 9. If, at the end of the year B's share of profit is tk 40,350, how much is the total profit?

Solution:
Let the total profit be P. The investments are in the ratio 5 : 6 : 9, so the total parts of the profit distribution will be,
5 + 6 + 9 = 20 parts

B's share corresponds to 6 parts,
⇒ 6/20 × P= 40,350
⇒ P =( 40350 × 20)/6
⇒ P = 6725 × 20
⇒ P = 134500

So the total profit is Tk 134,500.
৩০২.
A started a business with Tk. 42,000 and is joined afterwards by B with Tk. 72,000. After how many months did B join if the profits at the end of the year are divided equally?
  1. ক
    ক) 3 months
  2. খ
    খ) 4 months
  3. গ
    গ) 5 months
  4. ঘ
    ঘ) 6 months
ব্যাখ্যা
Suppose B joined after x months
then,
42000 × 12 = 72000 × (12 - x)
42 × 12 = 72 × (12 - x)
42 × 12 = 72 × 12 - 72x
72x = 864 - 504
⇒ 72x = 360
⇒ x = 5
৩০৩.
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. 920
  2. খ
    Tk. 1250
  3. গ
    Tk. 1065
  4. ঘ
    Tk. 1175
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. 

৩০৪.
Three partners A, B and C invest Tk.1500, Tk.1200, and Tk.1800 respectively in a company and make a profit of Tk.900. What is the amount of profit of C?
  1. ক
    ক) Tk.200
  2. খ
    খ) Tk.240
  3. গ
    গ) Tk.300
  4. ঘ
    ঘ) Tk.360
ব্যাখ্যা
প্রশ্ন: Three partners A, B and C invest Tk.1500, Tk.1200, and Tk.1800 respectively in a company and make a profit of Tk.900. What is the amount of profit of C?

সমাধান: 
A, B, C এর বিনিয়োগের অনুপাত = ১৫০০ : ১২০০ : ১৮০০
= ১৫ : ১২ : ১৮
= ৫ : ৪ : ৬

তারা লাভের পরিমাণকেও উক্ত অনুপাতে বণ্টন করবে।

অনুপাতের রাশিগুলোর যোগফল = ৫ + ৪ + ৬ = ১৫

C এর লাভের পরিমাণ = ৯০০ × (৬/১৫) টাকা 
= ৩৬০ টাকা 
৩০৫.
Tk. 1400 is divided among Aman, Belal and Shipon so that Aman receives half as much as Belal and Belal half as much as Shipon. Then Shipon's share is-
  1. ক
    Tk. 800
  2. খ
    Tk. 600
  3. গ
    Tk. 300
  4. ঘ
    Tk. 200
ব্যাখ্যা
Question: Tk. 1400 is divided among Aman, Belal and Shipon so that Aman receives half as much as Belal and Belal half as much as Shipon. Then Shipon's share is-

Solution:
Let Aman's share = Tk. x
Then
Belal's share = Tk. 2x
Shipon's share = Tk. 4x

Aman : Belal : Shipon = x : 2x : 4x = 1 : 2 : 4
Hence, Shipon's share = 1400 × (4/7) = Tk. 800
৩০৬.
A, B, C subscribe Tk. 50,000 for business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35,000, A receives-
  1. ক
    ক) 15000
  2. খ
    খ) 15500
  3. গ
    গ) 17400
  4. ঘ
    ঘ) 14700
ব্যাখ্যা
Question: A, B, C subscribe Tk. 50,000 for business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35,000, A receives-

Solution: 
Let
C subscribes = x.

Then,
B = x + 5000 and
A = x + 5000 + 4000
= x + 9000

So,
x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12

So A's Share = 35000×(21/50)
= 14700
৩০৭.
The price of a laptop is 50,000. How much do you need to pay if you get a 15% discount?
  1. ক
    Tk. 40000
  2. খ
    Tk. 42500
  3. গ
    Tk. 45000
  4. ঘ
    Tk. 41500
ব্যাখ্যা
Question: The price of a laptop is 50,000. How much do you need to pay if you get a 15% discount?

Solution:
For 15% discount,
Original price 100 paid price 85
∴ Original price 1 paid price 85/100
∴ Original price 50000 paid price (85 × 50000)/100
= 42500
৩০৮.
If a pen cost Tk. 50 after 10% discount, then what is the actual price or marked price (MP) of the pen?
  1. ক
    Tk. 50.55
  2. খ
    Tk. 60.66
  3. গ
    Tk. 55.55
  4. ঘ
    Tk. 50
ব্যাখ্যা
Question: If a pen cost Tk.50 after 10% discount, then what is the actual price or marked price (MP) of the pen?
 
Solution:
Since, we know;
MP - D = SP  ........(1)
where MP is marked price, D is discount, SP is selling price.
 
Percentage discount, D% = D/MP × 100
⇒ D = (D% × MP)/100 ........(2)
 
Substitute  value of D in (1).
MP - (D% × MP)/100 = SP
⇒ MP × (100 - D%)/100 = SP
 
Putting the given values in formula
MP × (100 - 10)/100 = 50
⇒ MP × (90/100) = 50
⇒ MP = (50 × 100)/90
∴ MP =  55.55
৩০৯.
A, B, and C started a business by investing Tk. 24,000, Tk. 32,000 and Tk. 40,000 respectively. If the total profit at the end of the year is Tk. 18,900, what is B's share of the profit?
  1. ক
    Tk. 5990
  2. খ
    Tk. 6300
  3. গ
    Tk. 6660
  4. ঘ
    Tk. 6800
ব্যাখ্যা

Question: A, B, and C started a business by investing Tk. 24,000, Tk. 32,000 and Tk. 40,000 respectively. If the total profit at the end of the year is Tk. 18,900, what is B's share of the profit?

Solution:
A, B এবং C এর বিনিয়োগের অনুপাত,
A : B : C = 24000 : 32000 : 40000
= 24 : 32 : 40
= 3 : 4 : 5

অনুপাতগুলোর যোগফল = 3 + 4 + 5 = 12

মোট লাভ = 18900 টাকা
B এর লভ্যাংশ = (B এর অনুপাত/অনুপাতগুলোর যোগফল) × মোট লাভ
= (4/12) × 18900
= (1/3) × 18900
= 6300 টাকা

সুতরাং, B এর লভ্যাংশ হল 6300 টাকা।

৩১০.
A man buys tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
  1. ক
    ক) 12
  2. খ
    খ) 15
  3. গ
    গ) 18
  4. ঘ
    ঘ) 21
ব্যাখ্যা

Dividend on tk. 20 = tk.9/100x 20= 9/5
tk.12 is an income on tk.100.
Tk. 9/5 is an income on tk. 100/12 x 9/5 = tk.15

৩১১.
Ajay and Vijay started a business together with an investment of Tk. (1400 + x) and (1800 + 2x). After a year, Vijay received a profit of Tk. 3200 out of total profit of Tk.5600. What is the initial investment of Ajay?
  1. ক
    Tk.2000
  2. খ
    Tk.1600
  3. গ
    Tk.1800
  4. ঘ
    Tk.1500
ব্যাখ্যা
Question: Ajay and Vijay started a business together with an investment of Tk. (1400 + x) and (1800 + 2x). After a year, Vijay received a profit of
Tk. 3200 out of total profit of Tk.5600. What is the initial investment of Ajay?

Solution:
Ratio of profit share = Ajay : Vijay
⇒ (1400 + x) : (1800 + 2x) = (5600 - 3200) : 3200
⇒ (1400 + x) /(1800 + 2x) = (5600-3200)/3200
⇒ (1400 + x) /(1800 + 2x) = 2400 / 3200
⇒ (1400 + x) /(1800 + 2x) = 3 / 4
⇒ 5600 + 4x = 5400 + 6x
⇒ 6x - 4x = 5600 - 5400
⇒ 2x = 200
∴ x= 100

∴ Initial investment of Ajay = 1400 + 100 = Tk.1500
৩১২.
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
    ক) 2% loss
  2. খ
    খ) 2% profit
  3. গ
    গ) 1% profit
  4. ঘ
    ঘ) 1% loss
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 cost price of goods = Tk. 100
Market price of goods
=110% of 100
=(110/100)×100
=Tk. 110

After discount selling price of goods
= 90% of 110
= (90/100) × 110
=Tk. 99

Loss = 100 - 99 = Tk. 1

Loss % = (1/100) × 100 = 1%
৩১৩.
A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?
  1. ক
    Tk 2400
  2. খ
    Tk 3000
  3. গ
    Tk 3200
  4. ঘ
    Tk 3400
ব্যাখ্যা
Question: A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?

Solution:
A invest 5000 for 3 months, 4500 for 4 months and 3600 for 5 months and gets a interest of 1000

ATQ,
{(5000 × R × 3)/(12 × 100)} + {(4500 × R × 4)/(12 × 100)} + {(3600 × R × 5)/(12 × 100)} = 1000
⇒ {(15000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} = 1000
⇒ (15000R/1200) + (18000R/1200) + (18000R/1200) = 1000
⇒  (51000R)/1200 = 1000
⇒ 51000R = 1200000
⇒ R = 1200000/51000
⇒  R=1200/51

For B,
{(P × 1200)/(51 × 1)}/100 = 800
⇒ (P × 1200/51)/100 = 800
⇒ (P × 1200)/51 = 80000
⇒  P × 1200 = 4080000
∴ P = 3400
৩১৪.
The marked price of a watch was Tk. 1500. A customer bought it for Tk. 1080 after getting two successive discounts. The first discount was 20%. What was the second discount rate?
  1. ক
    10%
  2. খ
    12%
  3. গ
    15%
  4. ঘ
    20%
ব্যাখ্যা

Question: The marked price of a watch was Tk. 1500. A customer bought it for Tk. 1080 after getting two successive discounts. The first discount was 20%. What was the second discount rate?

Solution:
Price after first discount (20%),
= 1500 - (20% of 1500)
= 1500 - (1500 × 0.20)
= 1500 - 300
= Tk. 1200

Amount of second discount
= 1200 − 1080
= Tk. 120

∴ Second discount rate
= (Second discount amount/Price after first discount) × 100
= (120/1200) × 100
= 0.10 × 100
= 10%

∴ The second discount rate is 10%.

৩১৫.
In a departmental store, an Tk. 400 dress is marked with Save 25%. What will be the sale price of this dress?
  1. ক
    Tk. 300
  2. খ
    Tk. 325
  3. গ
    Tk. 275
  4. ঘ
    Tk. 500
ব্যাখ্যা
Question: In a departmental store, an Tk. 400 dress is marked with Save 25%. What will be the sale price of this dress?

Solution:
The phrase, Save 25% (i.e. 0.25) , means discount rate.

The original price of the dress is given as Tk. 400.
The discount amount will be 0.25 × 400 = Tk.100

Sale price = 400 - 100 = Tk. 300
৩১৬.
A sells a scooter priced Tk. 36,000. He gives a discount of 8% on the first Tk. 20,000 and 5% on the next Tk. 10,000. How much discount can he offered on the remaining Tk. 6,000 if he is to get as much as when 7% discount is allowed on the total ?
  1. ক
    4%
  2. খ
    5%
  3. গ
    6%
  4. ঘ
    7%
ব্যাখ্যা
Question: A sells a scooter priced Tk. 36000. He gives a discount of 8% on the first Tk. 20000 and 5% on the next Tk. 10000. How much discount can he offered on the remaining Tk. 6000 if he is to get as much as when 7% discount is allowed on the total?

Solution:
Discount on Tk. 36000 = (36000 × 7)/100 = Tk. 2520
Discount on first Tk. 20000 = (20000 × 8)/100 = Tk. 1600
Discount on next Tk 10000 = (10000 × 5)/100 = Tk. 50

∴ Discount on remaining Tk. 6000 = {2520 - (1600 + 500)} = Tk. 420
So, Required percent = (420 × 100)/6000 = 7%
৩১৭.
Find the rate of discount being given on a shirt whose selling price is Tk.546 after deducting a discount of Tk.104 on its marked price. 
  1. ক
    18%
  2. খ
    10%
  3. গ
    16%
  4. ঘ
    20%
  5. ঙ
    None
ব্যাখ্যা

Question: Find the rate of discount being given on a shirt whose selling price is Tk.546 after deducting a discount of Tk.104 on its marked price.

Solution:
The price written on the item = 546 + 104 Tk.
= 650 Tk.

On 650 Taka, the commission is 104 Taka.
∴ Therefore, the commission on 100 Taka is (104 × 100)/650 Tk.
= 16 Tk.

৩১৮.
একটি কোম্পানি 'ক' মোট p টাকা লাভ করেছিল। লাভের অর্ধেক কোম্পানির প্রতিষ্ঠাতা পাওয়ার পর বাকি অর্ধেক সমানভাবে তাঁর চারজন অংশীদারের মধ্যে ভাগ করে দেয়া হয়। p-এর হিসেবে, প্রতিটি অংশীদার কত টাকা পেয়েছিলো?
  1. ক
    p/2
  2. খ
    p/6
  3. গ
    2p
  4. ঘ
    3p
  5. ঙ
    p/8
ব্যাখ্যা

প্রশ্ন: একটি কোম্পানি 'ক' মোট p টাকা লাভ করেছিল। লাভের অর্ধেক কোম্পানির প্রতিষ্ঠাতা পাওয়ার পর বাকি অর্ধেক সমানভাবে তাঁর চারজন অংশীদারের মধ্যে ভাগ করে দেয়া হয়। p-এর হিসেবে, প্রতিটি অংশীদার কত টাকা পেয়েছিলো?

সমাধান:
এখানে, কোম্পানি 'ক' এর মোট লাভ = p টাকা

প্রতিষ্ঠাতা পায় লাভের অর্ধেক  = p/2

∴ বাকি লাভ = (p − p/2) টাকা
= p/2 টাকা

বাকি অংশ 4 জন অংশীদারের মধ্যে সমানভাবে ভাগ করা হয়,
∴ প্রতিজন অংশীদার পায় = (p/2)/4
= (p/2) × (1/4)
= p/8

৩১৯.
A, B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000 resp. The respective share of A, B and C in an annual profit of Tk 40500 are.
  1. ক
    Tk. 10500, Tk. 12500, Tk. 16500
  2. খ
    Tk. 10500, Tk. 13500, Tk. 15500
  3. গ
    Tk. 10500, Tk. 13500, Tk. 16500
  4. ঘ
    Tk. 11500, Tk. 13500, Tk. 16500
ব্যাখ্যা
Question: A, B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000 resp. The respective share of A, B and C in an annual profit of Tk 40500 are.

Solution:
A : B : C = 35000 : 45000 : 55000
= 7 : 9 : 11
Now, we are having the ratio. to get the share, first make total of above ratio. then get each share.

A's Share = 40500 × (7/27) = Tk. 10500
B's Share = 40500 × (9/27) = Tk. 13500
C's Share = 40500 × (11/27) = Tk. 16500
৩২০.
The monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves BDT 30 per month, what would be the total amount of their monthly income?
  1. ক
    240
  2. খ
    300
  3. গ
    540
  4. ঘ
    600
ব্যাখ্যা
Question: The monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves BDT 30 per month, what would be the total amount of their monthly income?

Solution:
Let,
Their monthly income = 4a and 5a
Their monthly expenses = 7b and 9b

According to the conditions,
4a - 7b = 30 . . . . . (1)
5a - 9b = 30 . . . . . (2)

Multiply equation (1) and (2) by 9 and 7 respectively,
36a - 63b = 270 . . . .  (3)
35a - 63b = 210 . . . .  (4)

(3) - (2) ⇒
36a - 63b -35a + 63b = 270 - 210
⇒ a = 60

Hence, their total income = 4 × 60 + 5 × 60 tk
= 540

So, the total amount of their monthly income is 540 tk.
৩২১.
A shop is offering a 15% discount on a television whose original price is Tk. 40,000. What will be the selling price of the television after applying the discount?
  1. ক
    Tk. 24000
  2. খ
    Tk. 40000
  3. গ
    Tk. 44000
  4. ঘ
    Tk. 34000
  5. ঙ
    None
ব্যাখ্যা

Question: A shop is offering a 15% discount on a television whose original price is Tk. 40,000. What will be the selling price of the television after applying the discount?

Solution:
The original price of the television = Tk. 40000
And the discount percentage = 15%

We know,
Discount Amount = (Discount Percentage ÷ 100) × Original Price
= (15 ÷ 100) × 40000
= 6000

∴ Selling Price = 40000 - 6000 = 34000

The selling price after the discount is Tk. 34000.

৩২২.
A, B, and C invest in a business in the ratio 3 : 4 : 5. If the total profit is Tk 24,000, how much more did C get than A?
  1. ক
    Tk 3,600
  2. খ
    Tk 1,200
  3. গ
    Tk 4000
  4. ঘ
    Tk 4,800
ব্যাখ্যা

Question: A, B, and C invest in a business in the ratio 3 : 4 : 5. If the total profit is Tk 24,000, how much more did C get than A?

Solution:
→ Profit shares = 3x : 4x : 5x

Now
3x + 4x + 5x = 24000
12x = 24,000
→ x = 2,000

→ A’s share = 3 × 2,000 = 6,000
→ C’s share = 5 × 2,000 = 10,000
→ Difference = 10,000 - 6,000 = Tk 4,000

৩২৩.
Tk 30 is the true discount on Tk 330 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
  1. ক
    Tk. 15.71
  2. খ
    Tk. 13.67
  3. গ
    Tk. 17.67
  4. ঘ
    Tk. 12.33
  5. ঙ
    None
ব্যাখ্যা
Question: Tk 30 is the true discount on Tk 330 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Solution:
Simple Interest on Tk. (330 - 30) for a given time = Tk. 30
Simple Interest on Tk. 300 for half the time = Tk. 15
True Discount On Tk. 315 = Tk. 15
∴ True Discount On Tk. 330 = Tk. {(15/315) × 330}
= Tk. 15.71
৩২৪.
In a departmental store, a dress costs Tk. 400 and is marked with a 25% savings tag. What is the sale price of this dress?
  1. ক
    Tk. 200
  2. খ
    Tk. 300
  3. গ
    Tk. 350
  4. ঘ
    Tk. 400
ব্যাখ্যা
Question: In a departmental store, a dress costs Tk. 400 and is marked with a 25% savings tag. What is the sale price of this dress?

Solution:
The phrase, Save 25% (i.e. 0.25), means discount rate.

The original price of the dress is given as Tk. 400.
The discount amount will be 0.25 × 400 = Tk.100

Sale price = 400 - 100 = Tk. 300
৩২৫.
Tk. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have an equal amount of income. The investment in 9% stock is:
  1. ক
    ক) 4000
  2. খ
    খ) 4097
  3. গ
    গ) 5000
  4. ঘ
    ঘ) 5090
ব্যাখ্যা
Let the investment in 9% stock be Tk x.
Then, investment in 10% stock = Tk. (9800 - x).
(9/75) × X = 10/80 × (9800 - X)
3X/25 = (9800 - X)/8
24X = 9800 × 25 × -25X
49X = 9800 × 25
X = 5000
৩২৬.
X, Y, and Z share Tk. 1680 in such a way that X has 3.5 times as much as Y, and Y has 2 times as much as Z. How much money does Z receive?
  1. ক
    140 Tk.
  2. খ
    320 Tk.
  3. গ
    560 Tk.
  4. ঘ
    980 Tk.
  5. ঙ
    None
ব্যাখ্যা

Question: X, Y, and Z share Tk. 1680 in such a way that X has 3.5 times as much as Y, and Y has 2 times as much as Z. How much money does Z receive?

Solution:
Given,
X = 3.5Y
Y = 2Z

∴ X = 3.5 × 2Z = 7Z

So, the ratio of X, Y, Z = 7 : 2 : 1

∴ Z receive = [1680 × (1/10)] Tk.
= 168 Tk.

৩২৭.
You have saved 135 Taka by purchasing a blanket with 15% discount on it. what is the quoted price of the blanket in Taka?
  1. ক
    ক) 467
  2. খ
    খ) 900
  3. গ
    গ) 767
  4. ঘ
    ঘ) 1080
ব্যাখ্যা
15% ছাড়ে 
15 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা 
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/15 টাকা 
135 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 135)/15 টাকা 
                                                                      = 900 টাকা
৩২৮.
Moni and Mimi are partners in a business. Moni invests 36000 for 8 months and Mimi invests Tk 48000 for 10 months. Out of a profit of 32768, Moni's share is -
  1. ক
    ক) 20480
  2. খ
    খ) 16682
  3. গ
    গ) 14200
  4. ঘ
    ঘ) 12288
ব্যাখ্যা
Question: Moni and Mimi are partners in a business. Moni invests 36000 for 8 months and Mimi invests Tk 48000 for 10 months. Out of a profit of 32768, Moni's share is - 

Solution:
Ratio of their shares = (36000 × 8) : (48000 × 10)
= 288 : 480
= 3 : 5

Moni's share = 32768 × (3/8) = 12288
৩২৯.
A shopkeeper marks his goods 20% above cost price, but allows a 20% discount for cash payment. His net loss is?
  1. ক
    20%
  2. খ
    12%
  3. গ
    4%
  4. ঘ
    None of these
ব্যাখ্যা
Question: A shopkeeper marks his goods 20% above cost price, but allows a 20% discount for cash payment. His net loss is?

Solution:
Let
The cost price of goods = Tk. 100
Market price of goods = 120% of 100  
= 120/100 × 100
= Tk. 120

At 20% discount for cash payment, real price = (100 - 20)%
= 80%

After discount selling price of goods = 80% of 120
= Tk. 96
Loss = Tk. (100 - 96) = Tk. 4

∴ Loss % = (4/100) × 100 = 4%
৩৩০.
The contributions made by Rasel and Akash are in the ratio of 6 : 4. If 10% of the total profit is donated and Rasel gets 9000 as his share of profit, what is the total profit?
  1. ক
    15780.66
  2. খ
    16000.66
  3. গ
    16656.66
  4. ঘ
    16666.66
ব্যাখ্যা

Question: The contributions made by Rasel and Akash are in the ratio of 6 : 4. If 10% of the total profit is donated and Rasel gets 9000 as his share of profit, what is the total profit?

Solution:
Let,
the total profit after donated = p
The ratio of contribution by Rasel and Akash = 6 : 4
sum of ratios = 10

Rasel's share = (6/10) × p = 9000
⇒ p = (10 × 9000)/6
∴ p = 15000
so, total profit after donated = 15000

ATQ,
Rasel gets 9000 after 10% donated
Now,
90% = 15000
1% = 15000/90
And, 100% = (15000 × 100)/90 = 16,666.66

৩৩১.
A person invests in the stock market at 10% per annum, compounded annually, for 1 years. If the interest was compounded half-yearly, he would have received Tk. 75 more. Find the sum that invest in the stock market.
  1. ক
    ক) Tk. 20,000
  2. খ
    খ) Tk. 25,000
  3. গ
    গ) Tk. 30,000
  4. ঘ
    ঘ) Tk. 35,000
ব্যাখ্যা
When interest compounded annually, then person get 10% of the total sum
If interest compounded half-annually,
Interest rate = 5% and time t = 2

As we know, 5 + 5 + (5 × 5)/100 = 10.25%
If interest compounded half-annually, then person get 10.25% of the total sum

According to the question
⇒ 10.25% – 10% = 75
⇒ 0.25% = 75
⇒ 100% = 30,000

∴ The sum that invest in the stock market = Tk. 30000
৩৩২.
X and Y invest in business in the ratio 5 : 3. If 8% of the total profit goes to charity and X's share is Tk. 1380, the total profit is:
  1. ক
    Tk. 2400
  2. খ
    Tk. 2540
  3. গ
    Tk. 2620
  4. ঘ
    Tk. 2760
ব্যাখ্যা
Question: X and Y invest in business in the ratio 5 : 3. If 8% of the total profit goes to charity and X's share is Tk. 1380, the total profit is:

Solution:
Let the total profit be Tk. 100.
After paying to charity, X's share = (92 × 5/8) = 57.5
If X's share is Tk. 57.5, total profit = 100.
If X's share is Tk. 1380, total profit = (100/57.5 × 1380)
= 2400.
Therefore, the total profit is Tk. 2400.
৩৩৩.
A book costs Tk. 750. It is sold after giving three successive discounts of 20%, 15%, and 10%. Find the final price of the book after all discounts.
  1. ক
    Tk. 580
  2. খ
    Tk. 530
  3. গ
    Tk. 489
  4. ঘ
    Tk. 459
ব্যাখ্যা
Question: A book costs Tk. 750. It is sold after giving three successive discounts of 20%, 15%, and 10%. Find the final price of the book after all discounts.

Solution:
20% discount on 750 = 750 × 20% = Tk. 150

∴ Price after 20% discount = (750 - 150) = Tk. 600

Again,
15% discount on 600 = 600 × 15% = Tk. 90

∴ Price after 15% discount on Tk. 600 = (600 - 90) = Tk. 510

And,
10% discount on 510 = 510 × 10% = Tk. 51

∴ Price after 10% discount on Tk. 510 = (510 - 51) = Tk. 459

∴ the final price of the book after all discounts = Tk. 459
৩৩৪.
Man could not decide between discount of 30% or two successive discounts of 25% and 5%, both given on a shopping of Tk. 2,000. What is the difference between both the discounts?
  1. ক
    ক) Tk.54
  2. খ
    খ) Tk.37
  3. গ
    গ) Tk.25
  4. ঘ
    ঘ) Tk.21
ব্যাখ্যা
Question:  Man could not decide between discount of 30% or two successive discounts of 25% and 5%, both given on a shopping of Tk. 2,000. What is the difference between both the discounts?
Solution: 
বাজার খরচ = Tk. 2000

১ম শর্তমতে∶
শতকরা ছাড় = 30%
ছাড়  = 30% of 2000 = 30/100 × 2000 = Tk. 600

২য় শর্তমতে ∶
১ম শতাংশ ছাড় = 25%
১ম ছাড় = 25% of 2000 = 25/100 × 2000 = Tk. 500

প্রথম ছাড়ের পর বাজার খরচ = 2000 – 500 = Tk. 1500

২য় শতাংশ ছাড় = 5%
২য় ছাড় = 5/100 × 1500 = Tk. 75

সম্পূর্ণ ছাড় = 500 + 75 = Tk. 575

∴ উভয় শর্তে ছাড়  = 600 – 575 = Tk.25
৩৩৫.
Three partners shared the profit in a business in the ratio 3 : 4 : 5. They had partnered for 8 months, 6 months and 4 months respectively. What was the ratio of their investments?
  1. ক
    9 : 16 : 30
  2. খ
    9 : 18 : 30
  3. গ
    8 : 16 : 30
  4. ঘ
    9 : 16 : 24
  5. ঙ
    9 : 16 : 8
ব্যাখ্যা
Let their investments be x taka for 8 months,
                                        y taka for 6 months
                                 and z taka for 4 months respectively.

Then, 8x : 6y : 4z = 3 : 4 : 5.
or, 8x/6y = 3/4
or, y = 16x/9
and 8x/4z = 3/5.
or, z = 10x/3

x : y : z = x : 16x/9 : 10x/3 = 9 : 16 : 30
৩৩৬.
A person has deposited Tk. 13200 in a bank which pays 14% interest. He withdraws the money and invests in Tk. 100 stock at Tk. 110 which pays a dividend of 15%. How much does he gain or lose?
  1. ক
    ক) Loses Tk. 24
  2. খ
    খ) Gains Tk. 28
  3. গ
    গ) Loses Tk. 48
  4. ঘ
    ঘ) Gains Tk. 32
ব্যাখ্যা
Income from bank = 14% of Tk. 13200 = Tk. 1848
Number of shares purchased
= Tk. (13200/110)
= Tk. 120
Income from stock
= (15% of Tk. 100) × 120
= Tk. (15 × 20)
= Tk. 1800
∴ Loss = Tk. (1848 - 1800)
= Tk. 48
৩৩৭.
Three partners A, B, and C start a business. B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk 16500 at the end of a year, Find out A's share in it.
  1. ক
    6000
  2. খ
    9000
  3. গ
    11000
  4. ঘ
    12000
  5. ঙ
    None
ব্যাখ্যা
Question: Three partners A, B, and C start a business. B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk 16500 at the end of a year, Find out A's share in it.

Solution:
Let,
C's capital = x then
B's capital = 4x 
A's capital = 6x 

Now,
A : B : C = 6x : 4x : x
= 6 : 4 : 1

∴ A's share = 16500 × (6/11)
= 9000
৩৩৮.
Jamal started a partnership by investing Tk. 18,000. After 4 months, Hasan joined by investing Tk. x. If at the end of the year the profits are divided equally, find Hasan’s investment.
  1. ক
    Tk. 25000
  2. খ
    Tk. 27000
  3. গ
    Tk. 29500
  4. ঘ
    Tk. 31500
ব্যাখ্যা
Question: Jamal started a partnership by investing Tk. 18,000. After 4 months, Hasan joined by investing Tk. x. If at the end of the year the profits are divided equally, find Hasan’s investment.

Solution:
Given,
Jamal invests Tk. 18,000 for 12 months
∴ Jamal’s investment = 18,000 × 12 = 2,16,000

Hasan invests Tk. x for 8 months
∴ Hasan’s investment = 8x

ATQ,
216,000 : 8x = 1 : 1
⇒ 216,000/8x = 1/1
⇒ 8x = 216000
⇒ x = 216000/8
∴ x = 27000
৩৩৯.
On a 12% discount sale, an article costs Tk. 704. What was the original price of the article?
  1. ক
    Tk. 800
  2. খ
    Tk. 850
  3. গ
    Tk. 700
  4. ঘ
    Tk. 840
ব্যাখ্যা

Question: : On a 12% discount sale, an article costs Tk. 704. What was the original price of the article?

Solution:
Let the original price be Tk. x.

According to the question,
x - 12% of x = 704
⇒ x - (12x/100) = 704
⇒ (100x - 12x)/100 = 704
⇒ 88x = 70400
∴ x = 800

So, the original price of the article was Tk. 800.

৩৪০.
A, B, and C share Tk. 2,400 in such a way that A has 3 times as much as B, and B has 5 times as much as C. How much money (in taka) does C receive?
  1. ক
    108.67 tk
  2. খ
    114.29 tk
  3. গ
    123.37 tk
  4. ঘ
    129.72 tk
ব্যাখ্যা
Question: A, B, and C share Tk. 2,400 in such a way that A has 3 times as much as B, and B has 5 times as much as C. How much money (in taka) does C receive?

Solution:
Given,
A = 3B
and, B = 5C

Now, substituting B = 5C into A = 3B
A = 3 × 5C = 15C

So, the ratio of A : B : C becomes A : B : C = 15C : 5 C : C = 15 : 5 : 1
The total parts of the ratio are: 15 + 5 + 1 = 21

C's share = (1/21)× 2400
= 114.29 (approximately)

∴ C receives approximately Tk. 114.29.
৩৪১.
A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
  1. ক
    3 : 5 : 2
  2. খ
    6 : 10 : 5
  3. গ
    3 : 5 : 5
  4. ঘ
    3 : 5 : 6
  5. ঙ
    Data inadequate
ব্যাখ্যা
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

Solution:
Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x × 12) : (5x × 12) : (5x × 6) = 36 : 60 : 30 = 6 : 10 : 5.
৩৪২.
The contributions made by Rasel and Sejan are in the ratio of 3 : 2. If 5% of total profit is donated and Rasel gets 8550 as his share of profit, what is the total profit?
  1. ক
    14250
  2. খ
    14500
  3. গ
    15000
  4. ঘ
    15500
ব্যাখ্যা
Question: The contributions made by Rasel and Sejan are in the ratio of 3 : 2. If 5% of total profit is donated and Rasel gets 8550 as his share of profit, what is the total profit?

Solution:
Let the total profit after doneted = x
The ratio of contribution by Rasel and Sejan = 3 : 2
Sum of ratios = 5

Rasel's share = (3/5) × x = 8550
⇒ x = (8550 × 5)/3
∴ Total profit after doneted x = 14250

ATQ,
Rasel gets 8550 after 5 % donated
Now,
95% = 14250
1% = 14250/ 95
And, 100% = (14250/95) × 100 = 15000
৩৪৩.
Rahim and Karim enter into a partnership with capitals in the ratio of 10 : 12. At the end of 8 months, Rahim withdraws. If they receive profits in the ratio of 10 : 18. Find how long Karim's capital was used.
  1. ক
    7 months
  2. খ
    8 months
  3. গ
    10 months
  4. ঘ
    12 months
ব্যাখ্যা
Question: Rahim and Karim enter into a partnership with capitals in the ratio of 10 : 12. At the end of 8 months, Rahim withdraws. If they receive profits in the ratio of 10 : 18. Find how long Karim's capital was used.

Solution:
Let the capital of Rahim (C1) = 10
And the capital of Karim is (C2) = 12

Time period spend by Rahim (T1) = 8 months
Let, time period spend by Karim (T2) = x months

The ratio of their profit (p1 : p2) is 10 : 18
Apply formula:
(C1 × T1)/ (C2 × T2) = p1/p2
⇒ (10 × 8)/ (12 × x) = (10/18)
⇒ (80/12x) = (5/9)
⇒ 20/3x = 5/9
⇒ 180 = 15x
Hence, x = 12 months
৩৪৪.
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. 128
  2. খ
    Tk. 120
  3. গ
    Tk. 116
  4. ঘ
    Tk. 108
  5. ঙ
    None of the above
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
৩৪৫.
Mr.X gives 1/2 of his property to his wife and 1/2 of the rest to his son. The remainder is divided equally between his two daughters. The share of each daughter is-
  1. ক
    ক) 1/12 
  2. খ
    খ) 1/2 
  3. গ
    গ) 1/4 
  4. ঘ
    ঘ) 1/8 
ব্যাখ্যা
Let 
The whole property be 1
Share of wife =1/2
Remaining share= 1/2
Share of son = 1/2 of 1/2
                     = 1/4
Remaining share= (1/2) - (1/4)
                           = (2 - 1)/4
                           = 1/4
Share for each daughter =1/2 of 1/4
                                        =1/8
৩৪৬.
Find the cost price of a product. It is marked up by 45% more than the cost price and then a discount of 20% of marked price is given. Selling price is Tk. 4060.
  1. ক
    Tk. 3500
  2. খ
    Tk. 3600
  3. গ
    Tk. 3200
  4. ঘ
    Tk. 3800
ব্যাখ্যা
Question: Find the cost price of a product. It is marked up by 45% more than the cost price and then a discount of 20% of marked price is given. Selling price is Tk. 4060.

Solution:
Let,
Cost price be Tk. 100

Marked price = Tk. 100 + Tk. 45
= Tk. 145

Discount = 20% of marked price
∴ Selling price = (100 - 20) % of marked price = 80% of of marked price
= 80% of Tk. 145 
= Tk. 116

Selling price 116 when cost price 100
∴ Selling price 1 when cost price 100/116
∴ Selling price 4060 when cost price (100 × 4060)/116
= Tk. 3500
৩৪৭.
A person paid Tk. 17000 for a motor-car after a single discount of 15%. If he is given successive discount of 5% and 10% then how much he would pay?
  1. ক
    ক) 17000
  2. খ
    খ) 17010
  3. গ
    গ) 17100
  4. ঘ
    ঘ) 18900
ব্যাখ্যা

Cost price of motor-car = Tk. 17000
Mark price of motor-car
= Tk 17000 × 100/85 = Tk. 20000
After successive discount,Cost price
= Tk. 20000 × 95/100×90/100
= Tk. 17100 

৩৪৮.
1/4 of Ram's money is equal to 1/6 of Shyam's money. If both together have Tk. 600 the difference between their amounts is-
  1. ক
    ক) 50
  2. খ
    খ) 120
  3. গ
    গ) 240
  4. ঘ
    ঘ) 360
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
শ্যামের টাকা x হলে রামের টাকা (600 - x) টাকা।
প্রশ্নমতে, 1/4(600-x) = x/6
⇒6(600 - x) = 4x
⇒ 10x = 3600
⇒ x = 360
তাহলে রামের টাকা 600 - 360 = 240
সুতরাং তাদের টাকার পার্থক্য 360 - 240 = 120 টাকা।
৩৪৯.
Meena and Raju started a business with investments of Tk. (2000 + x) and Tk. (3000 + 2x) respectively. After a year, Raju received a profit of Tk. 4800 out of a total profit of Tk. 8000. Find the value of Meena's investment.
  1. ক
    Tk. 4000
  2. খ
    Tk. 3000
  3. গ
    Tk. 2500
  4. ঘ
    Tk. 2000
ব্যাখ্যা
Question: Meena and Raju started a business with investments of Tk. (2000 + x) and Tk. (3000 + 2x) respectively. After a year, Raju received a profit of Tk. 4800 out of a total profit of Tk. 8000. Find the value of Meena's investment.

Solution:
Given,
Raju’s profit = Tk. 4800
∴ Meena’s profit = Tk. (8000 - 4800)
= Tk. 3200

Given,
Meena : Raju = 3200 : 4800
⇒ (2000 + x) : (3000 + 2x) = 3200 : 4800
⇒ (2000 + x)/(3000 + 2x) = 3200/4800
⇒ (2000 + x)/(3000 + 2x) = 2/3
⇒ 3(2000 + x) = 2(3000 + 2x)
⇒ 6000 + 3x = 6000 + 4x
⇒ 4x - 3x = 6000 - 6000
∴ x = 0

∴ Initial investment of Meena = 2000 + 0 = Tk. 2000
৩৫০.
What is the discount rate percentage on a gift whose selling price is Tk. 440 after a reduction of Tk. 60 on its marked price?
  1. ক
    12%
  2. খ
    15%
  3. গ
    16%
  4. ঘ
    20%
ব্যাখ্যা
Question: What is the discount rate percentage on a gift whose selling price is Tk. 440 after a reduction of Tk. 60 on its marked price?

Solution: 
Given,
SP of the gift = Tk. 440
Discount = Tk. 60

MP of the gift = Tk. (440 + 60) = Tk. 500

∴ Discount percentage = (60/500) × 100 = 12%
৩৫১.
Raju started a business with Tk. 900. Kamal joined him after few months with an amount of 600. If the profits at the end of the year were divided in the ratio of 2 : 1, after how many months Kamal joined the business?
  1. ক
    9 months
  2. খ
    3 months
  3. গ
    8 months
  4. ঘ
    6 months
ব্যাখ্যা
Question: Raju started a business with Tk. 900. Kamal joined him after few months with an amount of 600. If the profits at the end of the year were divided in the ratio of 2 : 1, after how many months Kamal joined the business?

Solution:
The capital of Raju (C1) = 900
And the capital of Kamal is (C2) = 600

Time period spend by Raju (T1) = 12 months
Let the time period spend by Kamal (T2) = x months

The ratio of their profit (p1 : p2) is 2 : 1

Apply the formula:
(C1 × T1)/ (C2 × T2) = p1/p2
(900 × 12)/ (600 × x) = (2/1)
10800/600 = 2 × x
x = 18/2
x = 9 

i.e., Kamal spend 9 months.
So, Kamal joined after, 12 - 9 = 3 months.
৩৫২.
The present worth of a sum due sometime hence is Tk. 576 and the banker's gain is Tk. 16. The true discount is
  1. ক
    ক) Tk. 36
  2. খ
    খ) Tk. 72
  3. গ
    গ) Tk. 48
  4. ঘ
    ঘ) Tk. 96
ব্যাখ্যা
প্রশ্ন: The present worth of a sum due sometime hence is Tk. 576 and the banker's gain is Tk. 16. The true discount is

সমাধান: 
True discount = √(present worth  ×  banker's gain)
= √(576 × 16)
= √9216
= 96.
৩৫৩.
Sourav and Fahim started a business by investing Tk. 4000 and Tk. 3000 respectively. After 6 months, Arif joined them by investing Tk. 4000. At the end of 2 years, they earned a profit of Tk. 5000 then what will be Fahim's share?
  1. ক
    Tk.1200
  2. খ
    Tk.1500
  3. গ
    Tk.1900
  4. ঘ
    Tk.1300
ব্যাখ্যা

Sourav invests Tk. 4000 for 24 months, Fahim invests Tk. 3000 for 24 months and Arif invests
Tk. 4000 for 18 months.
Then,
Sourav:Fahim:Arif = (4000x24):(3000x24):(4000x18)
= 4x24 : 3x24 : 4x18
= 4 : 3 : 3
Therefore, Fahim's share = Tk. 5000 x 3/10
= Tk. 1500.

৩৫৪.
Rina ,Ratul and Ayesha started a business. Rina invested 1/3 part, Ratul 1/4 part and rest of the capital was invested by Ayesha. The ratio of their profits will be-
  1. ক
    3 : 4 : 5
  2. খ
    5 : 4 : 3
  3. গ
    4 : 3 : 5
  4. ঘ
    4 : 5 : 3
ব্যাখ্যা

Question: Rina ,Ratul and Ayesha started a business. Rina invested 1/3 part, Ratul 1/4 part and rest of the capital was invested by Ayesha. The ratio of their profits will be-

Solution:
Let,
Total capital be TK x
Then,
Rina's share = x/3 TK
Ratul's share = x/4 TK
Ayesha's share = x - {(x/3) + (x/4)}
= x - {(4x + 3x)/12}
= x - (7x/12)
= (12x - 7x)/12
= 5x/12 TK

∴ Required ratio
= (x/3) : (x/4) : (5x/12)
= 4x : 3x : 5x     [multiply by 12]
= 4 : 3 : 5

৩৫৫.
Yesterday, a shop made Tk. 5,000 in total sales. One-fifth of these sales came from items that were sold at a 20% discount.What would the shop’s total sales have been yesterday if all items had been sold at full price?
  1. ক
    Tk. 5200
  2. খ
    Tk. 5250
  3. গ
    Tk. 5300
  4. ঘ
    Tk. 5400
ব্যাখ্যা

Question: Yesterday, a shop made Tk. 5,000 in total sales. One-fifth of these sales came from items that were sold at a 20% discount. What would the shop’s total sales have been yesterday if all items had been sold at full price?


Solution:
Total sales = Tk. 5,000
Discounted sales = 1/5 of 5,000 = 1,000

Since these items were sold at 20% discount,
The full price of these items = 1,000 ÷ (1 - 0.20) = 1,000 ÷ 0.8 = Tk. 1,250
Sales from items not discounted = 5,000 - 1,000 = Tk. 4,000

If all items were sold at full price, total sales
= 4,000 + 1250
= Tk. 5250

৩৫৬.
A and B start a business with initial investment in the ratio 12 : 11 and their annual profits were in the ratio 4 : 1. If A invested the money for 11 months B invested the money for –
  1. ক
    ক) 3 months
  2. খ
    খ) 4 months
  3. গ
    গ) 5 months
  4. ঘ
    ঘ) 6 months
ব্যাখ্যা

Let, B invested the money for t months
Then the ratio of investment = (12×11 : 11× t) = 12 : t
So, 12/t = 4/1
⇒ t = 3 months

৩৫৭.
On a 20% discount sale, an article costs Tk. 596. What was the original price of the article? 
  1. ক
    Tk. 775
  2. খ
    Tk. 745
  3. গ
    Tk. 735
  4. ঘ
    Tk. 720
  5. ঙ
    None of these
ব্যাখ্যা
Question: On a 20% discount sale, an article costs Tk. 596. What was the original price of the article?

Solution:
If the selling price of the article is S, then
S - 20% of S = 596
⇒ S - S/5 = 596
⇒ 4S/5 = 596
⇒ S = (596 × 5)/4
∴ S = 745
৩৫৮.
Two partners invest TK 1,00,000 and TK 60,000 .After 6 months, they admit a new partner with TK 80,000. What is the ratio of their profits after one year?
  1. ক
    6 : 4 : 5
  2. খ
    5 : 4 : 6
  3. গ
    5 : 3 : 2
  4. ঘ
    2 : 3 : 5
ব্যাখ্যা

Question: Two partners invest TK 1,00,000 and TK 60,000 .After 6 months, they admit a new partner with TK 80,000. What is the ratio of their profits after one year?

Solution:
Profit sharing ratio depends on : Capital × Time
Let,
the partners be P, Q and R

P's invest : TK 1,00,000 for 12 months
⇒ 1,00,000 × 12 = 12,00,000

Q's invest : TK 60,000 for 12 months

⇒ 60,000 × 12 =7,20,000

R's invest: TK 80,000 for 6 months

⇒ 80,000 × 6 = 4,80,000

Now, the ratio of profits:
12,00,000 : 7,20,000 : 4,80,000

Simplify = 5 : 3 : 2

∴ Ratio = 5 : 3 : 2

৩৫৯.
The investment ratio of two partners, A and B, is 11 : 12, while their profit ratio is 2 : 3. Given that A invested his funds for 8 months, determine the duration of B's investment.
  1. ক
    12 months
  2. খ
    9 months
  3. গ
    10 months
  4. ঘ
    11 months
ব্যাখ্যা

Question: The investment ratio of two partners, A and B, is 11 : 12, while their profit ratio is 2:3. Given that A invested his funds for 8 months, determine the duration of B's investment.

Solution:
Let, A invested Tk 11x for 8 months
and B invested Tk 12x for y months

Now,
(11x × 8) : (12x × y) = 2 : 3
⇒ (11x × 8) / (12x × y) = 2/3
⇒ 88x/12xy = 2/3
⇒ 24y = 264
⇒ y = 11

So, B invested for 11 months. 

৩৬০.
What is the banker’s discount, if the true discount on a bill of Tk. 840 is Tk.105?
  1. ক
    ক) 100
  2. খ
    খ) 110
  3. গ
    গ) 120
  4. ঘ
    ঘ) 130
ব্যাখ্যা

Present Worth (P.W.) = 840 - 105 
= Tk. 735
Therefore, S.I. on Tk. 735 = Tk. 105
S.I. on Tk. 8400
= 105 × 840/735
= Tk. 120

৩৬১.
A, B, and C enter into a partnership. A contributes one-third of the capital while C contributes as much as A and B together contribute. If the profit at the end of the year amounts to Tk.19800, what would B receive?
  1. ক
    9400 Tk.
  2. খ
    3300 Tk.
  3. গ
    5800 Tk.
  4. ঘ
    6100 Tk.
ব্যাখ্যা
Question: A, B, and C enter into a partnership. A contributes one-third of the capital while C contributes as much as A and B together contribute. If the profit at the end of the year amounts to Tk.19800, what would B receive?

Solution: 
As C contributes as much as A and B,
∴ C's share is = 1/2
A's share = 1/3
B's share = ( 1 - 1/3 - 1/2) = 1/6

∴ B will receive = 1/6(19800) = 3300 Tk.
৩৬২.
The single discount which is equivalent to discount of 10%, 20% and 25% is -
  1. ক
    34%
  2. খ
    46%
  3. গ
    28%
  4. ঘ
    32%
ব্যাখ্যা
Question: The single discount which is equivalent to discount of 10%, 20% and 25% is -

Solution:
Let marked price be 100%.
⇒ S.P = (90/100) × (80/100) × (75/100) × 100
⇒ S.P = 54%

Discount will be 100 – 54 = 46%

∴ The single discount will be 46%
৩৬৩.
A company pays 12.5% dividend to its investors. If an investor buys tk.50 shares and gets 25% on investment, at what price did the investor buy the shares?
  1. ক
    ক) 6.25
  2. খ
    খ) 25
  3. গ
    গ) 50
  4. ঘ
    ঘ) 12.5
ব্যাখ্যা

Dividend on 1 share = (12.5 x 50)/100 = tk.6.25
tk.25 is income on an investment of tk.100
tk.6.25 is income on an investment of tk. (6.25 x 100)/25 = tk.25

৩৬৪.
A and B invest in business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share in Tk. 1710, the total profit is:
  1. ক
    Tk. 3,300
  2. খ
    Tk. 1,100
  3. গ
    Tk. 1,700
  4. ঘ
    Tk. 3,000
ব্যাখ্যা
Question: A and B invest in business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share in Tk. 1710, the total profit is:

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

If A's share is Tk. 57, total profit = 100.
If A's share is Tk. 855, total profit = (100/57 × 1710)
= Tk. 3,000
৩৬৫.
The true discount on Tk. 2562 due 4 months hence is Tk. 122. What is the rate percent?
  1. ক
    12%
  2. খ
    13%
  3. গ
    15%
  4. ঘ
    14%
ব্যাখ্যা

Question: The true discount on Tk. 2562 due 4 months hence is Tk. 122. What is the rate percent?

Solution: 
Given,
Amount (A) = 2562 Tk
True Discount (TD) = 122 Tk
Time (T) = 4 months = 1/3 of a year

Present Worth, P.W. = (2562−122) Tk
= 2440 Tk

True Discount (TD) = Simple Interest (SI) on the Present Worth (PW) for the given time period.
∴ S.I. on 2440 Tk for 4 months is 122 Tk.

We know, SI = PRT/100
∴ R = (SI × 100)/(P × T)
= [(100 × 122)/(2440 × (1/3)]
= 15

∴ Rate is 15%

 

৩৬৬.
X, Y, Z subscribe Tk. 50,000 for a business. X subscribes Tk. 4000 more than Y and Y Tk. 5000 more than Z. Out of a total profit of Tk. 35,000, X receives-
  1. ক
    Tk. 14,700
  2. খ
    Tk. 12,700
  3. গ
    Tk. 14,500
  4. ঘ
    Tk. 11,700
  5. ঙ
    None of the above
ব্যাখ্যা
Question: X, Y, Z subscribe Tk. 50,000 for a business. X subscribes Tk. 4000 more than Y and Y Tk. 5000 more than Z. Out of a total profit of Tk. 35,000, X receives-

Solution:
Let, Z subscribes p taka
Y subscribes p + 5000 taka
X subscribes p + 5000 + 4000
= p + 9000 taka

p + p + 5000 + p + 9000 = 50000
⇒ 3p + 14000 = 50000
⇒ 3p = 36000
⇒ p = 12000 taka

X receives = {(p + 9000)/50000} × 35000
= (21000/50000) × 35000
= 14700 taka
৩৬৭.
A sum of money is to be divided among P, Q, R, S in the ratio 7 : 3 : 5 : 2. If R gets Tk. 2000 more than S, what is Q's share?
  1. ক
    Tk. 3100
  2. খ
    Tk. 2000
  3. গ
    Tk. 2200
  4. ঘ
    Tk. 2300
ব্যাখ্যা

Question: A sum of money is to be divided among P, Q, R, S in the ratio 7 : 3 : 5 : 2. If R gets Tk. 2000 more than S, what is Q's share?

Solution:
Let their shares be 7x, 3x, 5x, and 2x respectively.

ATC,
5x - 2x = 2000
⇒ 3x = 2000
⇒ x = 2000/3

Therefore,
Q's share = 3x
= 3 × (2000/3)
= 2000 taka.

৩৬৮.
A, B and C started a business with the investment of Tk.4000, Tk.3000 and Tk.2000 respectively. At the end of the year, the profit received by B and C together is Tk.1500 more than the profit received by A. What is the total profit of the business?
  1. ক
    Tk.13500
  2. খ
    Tk.12480
  3. গ
    Tk.11350
  4. ঘ
    Tk.15550
ব্যাখ্যা
Question: A, B and C started a business with the investment of Tk.4000, Tk.3000 and Tk.2000 respectively. At the end of the year, the profit received by B and C together is Tk.1500 more than the profit received by A. What is the total profit of the business?

Solution:
 বিনিয়োগের অনুপাত, A : B : C = 4000 : 3000 : 2000 = 4 : 3 : 2

ধরি, মোট লাভ = x টাকা
সুতরাং,
A এর লাভ = 4​x/9
B এবং C এর একত্রে লাভ = (3x/9) + (2x/9) = 5x/9

প্রশ্নমতে,
⇒ 5x/9 = (4​x/9) + 1500
⇒ (5x/9) - (4​x/9) = 1500
⇒ (5x - 4x)/9 = 1500
⇒ x/9 = 1500
⇒ x = 1500 × 9
⇒ x = 13500

∴ মোট লাভ 13500
৩৬৯.
A man invests in a 16% stock at 128. The interest obtained by him is?
  1. ক
    ক) 10%
  2. খ
    খ) 12.5%
  3. গ
    গ) 6 %
  4. ঘ
    ঘ) 15%
ব্যাখ্যা
Question: A man invests in a 16% stock at 128. The interest obtained by him is?

Solution:
By investing Tk. 128, income derived = Tk. 16
By investing Tk. 100, income derived
= Tk. (16/128) × 100
= Tk. 12.5

∴ Interest obtained = 12.5%
৩৭০.
Labib started a business with Tk. 2100 and is joined afterward by Shishir with Tk. 3600. After how many months did Shishir join if the profits at the end of the year are divided equally?
  1. ক
    4 months
  2. খ
    5 months
  3. গ
    6 months
  4. ঘ
    7 months
ব্যাখ্যা
Question: Labib started a business with Tk. 2100 and is joined afterward by Shishir with Tk. 3600. After how many months did Shishir join if the profits at the end of the year are divided equally?

Solution:
Suppose,
Shishir joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ Shishir joined after 5 months
৩৭১.
Kamal and Rajon enter into a partnership with their capitals in the ratio 5 : 6. At the end of 6 months Kamal withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long was Rajon's capital used?
  1. ক
    11 months
  2. খ
    10 months
  3. গ
    8 months
  4. ঘ
    None of these
ব্যাখ্যা

Question: Kamal and Rajon enter into a partnership with their capitals in the ratio 5 : 6. At the end of 6 months Kamal withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long was Rajon's capital used?

Solution: 
Let,
Kamal invested Tk. 5x for 6 months
And
Rajon invested Tk. 6x for y months
Then,
(5x × 6)/(6x × y) = 5/9
⇒ 30x/6xy = 5/9
⇒ 5/y = 5/9
∴ y = 9

So Rajon capital was used for 9 months

৩৭২.
Rana and Rahim invest TK 30,000 and 40,000 respectively in a partnership. They earned a profit of TK 7000. Find Rana's share of the profit
  1. ক
    TK 3500
  2. খ
    TK 4000
  3. গ
    TK 3000
  4. ঘ
    TK 4500
ব্যাখ্যা

Question: Rana and Rahim invest TK 30,000 and 40,000 respectively in a partnership. They earned a profit of TK 7000. Find Rana's share of the profit.

Solution:
Given that,
Investment ratio = 30,000 : 40,000
= 3 : 4

sum of  the ratio's = 3 + 4 = 7
∴ Rana's share of the profit = 7000 × (3/7)
= 1000 × 3
= 3000 tk

৩৭৩.
Asif and Himel are partners in a business. Asif invests Tk. 30000 for 6 months and Himel invest Tk. 36000 for 9 months. What is Asif's share out of a profit of Tk. 26600?
  1. ক
    ক) Tk. 8750 
  2. খ
    খ) Tk. 9500 
  3. গ
    গ) Tk. 10300 
  4. ঘ
    ঘ) Tk. 11500 
ব্যাখ্যা
Question: Asif and Himel are partners in a business. Asif invests Tk. 30000 for 6 months and Himel invest Tk. 36000 for 9 months. What is Asif's share out of a profit of Tk. 26600?

Solution: 
Ratio of their shares = (30000 × 6) : (36000 × 9)
= (30 × 6) : (36 × 9)
= 5 : 9

Asif's share,
= (26600 × 5)/14
= Tk. 9500
৩৭৪.
Mobin buys 100 shares of par value Tk. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
  1. ক
    ক) Tk. 6
  2. খ
    খ) Tk. 8
  3. গ
    গ) Tk. 4
  4. ঘ
    ঘ) Tk. 10
ব্যাখ্যা
Face value of each share = Tk. 5
Total dividend received by Mobin = {100 × 5 × (12/100)}
= Tk. 60
Let market value of 100 shares = Tk. x
x × (10/100) = 60
x = 600
ie, Market value of 100 shares = Tk. 600
Hence, Market value of each share = Tk. 6
৩৭৫.
Taposh purchased an mp3 player, originally priced at Tk. 2900, but discounted by Tk. 270. What percent discount did Taposh receive on the mp3 player?
  1. ক
    14%
  2. খ
    5%
  3. গ
    9.3%
  4. ঘ
    9%
ব্যাখ্যা
Question: Taposh purchased an mp3 player, originally priced at Tk. 2900, but discounted by Tk. 270. What percent discount did Taposh receive on the mp3 player?

Solution:
percent discount = (270/2900) × 100%
= 9.31%
৩৭৬.
A man bought 20 shares of Tk. 50 at 5 discount, the rate of dividend being 13(1/2). The rate of interest obtained is:
  1. ক
    ক) 10%
  2. খ
    খ) 12(1/2)%
  3. গ
    গ) 17(3/4)%
  4. ঘ
    ঘ) 24%
  5. ঙ
    ঙ) 15%
ব্যাখ্যা

Investment = Tk.[20 × (50 − 5)] = Tk. 900.
FaceValue = Tk. (50 × 20) = Tk.1000.
Dividend = Tk. (27/2 × 1000/100) = Tk.135.
Interest Obtained = (135/900 × 100)% = 15%

৩৭৭.
A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash payment. His net loss is?
  1. ক
    ক) 12%
  2. খ
    খ) 16%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Let the cost price of goods = Tk. 100
Market price of goods = 120% of 100  
                                     = 120/100×100
                                     = Tk. 120
At 30% discount for cash payment, real price = (100 - 30)% = 70%
After discount selling price of goods
= 70% of 120
= Tk. 84
Loss = Tk. (100 − 84) = Tk. 16
Loss % = (16/100) × 100 = 16%
৩৭৮.
A man buys 50 taka shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares ?
  1. ক
    30
  2. খ
    35
  3. গ
    40
  4. ঘ
    45
  5. ঙ
    50
ব্যাখ্যা
Dividend on 1 share = 50 × 10% = 5
12.50 taka is an income on an investment of 100 taka
5 taka is an income on an investment of (100 × 5/12.50) taka = 40 taka
∴ Cost of 1 share = 40 taka
৩৭৯.
The marked price of a mobile is 20% more than its cost price. If a discount of 10% is given on the marked price, the profit percent is:
  1. ক
    8%
  2. খ
    10%
  3. গ
    12%
  4. ঘ
    20%
ব্যাখ্যা
Question: The marked price of a mobile is 20% more than its cost price. If a discount of 10% is given on the marked price, the profit percent is:

Solution:
Let,
Cost price = Tk.100
 
Market price = 100 + 20% of 100
= 100 + (100 × 20/100)
= Tk. 120
 
Now,
Selling price  = 120 - 10% of 120
= 120 - (120 × 10)/100
= Tk. 108
 
Profit = 108 - 100 = Tk. 8
∴ Profit % = (8 × 100)/100
= 8%
৩৮০.
1740 is divided among A, B, and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then C will get
  1. ক
    348 tk
  2. খ
    464 tk
  3. গ
    528 tk
  4. ঘ
    696 tk
ব্যাখ্যা
Question: 1740 is divided among A, B, and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then C will get

Solution:
A × 0.5 = B × 0.6 = C × 0.75
⇒ (A × 5)/10 = (B × 6)/10 = (C × 75)/100
⇒ A/2 = B/(5/3) = C/(4/3)
⇒ A : B : C = 2 : (5/3) : (4/3)
⇒ A : B : C = 6 : 5 : 4

∴ C’s share = (4/15) × 1740 = 464 tk
৩৮১.
A “Buy 3, Get 1 Free” deal is available at a store. How much discount does this equal in percentage terms?
  1. ক
    16%
  2. খ
    25%
  3. গ
    30%
  4. ঘ
    20%
ব্যাখ্যা

Question: A “Buy 3, Get 1 Free” deal is available at a store. How much discount does this equal in percentage terms?

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%.

৩৮২.
P, Q and R start a business. P invests 3 times as much as Q invests 2/3rd as much as R invests. Find the ratio of capitals of P, Q and R ? 
  1. ক
    ক) 3 : 2 : 6
  2. খ
    খ) 6 : 2 : 3
  3. গ
    গ) 2 : 6 : 3
  4. ঘ
    ঘ) 5 : 2 : 3
ব্যাখ্যা
ধরি 
R বিনিয়োগ করে = x টাকা 
Q বিনিয়োগ করে = 2x/3 টাকা 
P বিনিয়োগ করে = 3× (2x/3) টাকা
                          = 2x টাকা 
P, Q এবং R এর বিনিয়োগের অনুপাত = 2x : (2x/3) : x
                                                          = 2 : (2/3) : 1
                                                           = 6 : 2 : 3
৩৮৩.
Tk. 2100 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is -
  1. ক
    ক) 300
  2. খ
    খ) 600
  3. গ
    গ) 1200
  4. ঘ
    ঘ) 1800
ব্যাখ্যা
Question: Tk. 2100 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is - 

Solution:
ধরি, A পাবে ক টাকা
B পাবে ২ক টাকা
C পাবে ৪ক টাকা

প্রশ্নমতে,
ক + ২ক + ৪ক = ২১০০
৭ক = ২১০০
ক = ৩০০

∴ C পাবে = ৪ × ৩০০ = ১২০০
৩৮৪.
A starts business with tk. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in a ratio 2 : 3. What is B's contribution in the capital?
  1. ক
    7500
  2. খ
    8000
  3. গ
    8500
  4. ঘ
    9000
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 in the ratio 2 : 3. What is B's contribution in the capital?

Solution: 
Let B's capital be tk. x.
Then, (3500 x 12)/7x = 2/3
⇒14x = 126000
⇒ x = 9000 tk
৩৮৫.
P, Q, R enter into partnership. P invests 3 times as much as Q invests and Q invests two third of what R invests. At the end of the year, the profit earned is TK. 6600. What is the share of R?
  1. ক
    Tk. 1200
  2. খ
    Tk. 1400
  3. গ
    Tk. 1800
  4. ঘ
    Tk. 2000
ব্যাখ্যা
Question: P, Q, R enter into partnership. P invests 3 times as much as Q invests and Q invests two third of what R invests. At the end of the year, the profit earned is TK. 6600. What is the share of R?

Solution:
P invests 3 times as much as Q invests and Q invests two third of what R invests.

Let,
R invests = x
Q invests = 2x/3
P invests = 3 × (2x/3) = 2x

The ratio of invests or profit 2x: 2x/3: x
= 6x : 2x : 3x
= 6 : 2 : 3

∴ The share of R =  (3/11) × 6600
= 1800
৩৮৬.
A bicycle marked at Tk. 4,000, is sold with two successive discount of 20% and 10%. An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:
  1. ক
    ক) Tk. 3444
  2. খ
    খ) Tk. 2842
  3. গ
    গ) Tk. 2736
  4. ঘ
    ঘ) Tk. 2632
ব্যাখ্যা
Question: A bicycle marked at Tk. 4,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:

Solution: 
Marked Price = 4000
SP after first Discount of 20% = 4000 - 20% of 4000 = 3200
SP after second Discount of 10% = 3200 - 10% of 3200 = 2880
Now, the final selling price at cash = 2880 - 5% of 2880 = Tk. 2736
৩৮৭.
Two friends invested TK.1500 and TK. 3500 in a business. They earned a profit of TK. 1000. One-half of the profit was divided equally between them and the other half was divided in proportion to their capitals. How much did each of them receive ?
  1. ক
    TK. 350 and TK. 450
  2. খ
    TK. 450 and TK. 650
  3. গ
    TK. 400 and TK. 600
  4. ঘ
    TK. 600 and TK. 400
ব্যাখ্যা

Question: Two friends invested TK.1500 and TK. 3500 in a business. They earned a profit of TK. 1000. One-half of the profit was divided equally between them and the other half was divided in proportion to their capitals. How much did each of them receive ?

Solution:
Ratio of shares
= 1500 : 3500
= 3 : 7

Share of first friend
= TK. [(500/2) + {500 × (3/10)}]
= TK.[250 + 150]
= TK. 400

Share of second friend
= TK. [(500/2) + {500 × (7/10)}]
= TK.[250 + 350]
=  TK. 600

৩৮৮.
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. 35,000, C receives:
  1. ক
    ক) 7200 Tk
  2. খ
    খ) 8200 Tk
  3. গ
    গ) 8400 Tk
  4. ঘ
    ঘ) 6200 Tk
ব্যাখ্যা
Let C = x.
Then, B = x + 5000
A = x + 5000 + 4000
    = x + 9000.

So,
x + x + 5000 + x + 9000 = 50000
3x = 36000
 x = 12000

A : B : C = 21000 : 17000 : 12000
              = 21 : 17 : 12

C's share = 35000 × 12/50 = Tk. 8400
৩৮৯.
A clothing store offers a dress initially at $100. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?
  1. ক
    $68
  2. খ
    $66
  3. গ
    $60
  4. ঘ
    $65
ব্যাখ্যা
Question: A clothing store offers a dress initially at $100. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?

Solution:
For the first discount, we have 100(1 - 0.15) = 100(0.85) = 85.
So the dress is worth $85
After the second discount, we have 85(1 - 0.20) = 85(0.8) = 85 × (4/5) = 17 × 4 = 68
So the final dress price is $68
৩৯০.
Rahim, Karim, and Masum started a business by investing Tk.150000, Tk.120000, and Tk.135000 respectively. Find the share of Karim out of the annual profit of Tk. 56700?
  1. ক
    ক) Tk. 18,900
  2. খ
    খ) Tk. 16,800
  3. গ
    গ) Tk. 21,000
  4. ঘ
    ঘ) Tk. 17,900
ব্যাখ্যা
Question: Rahim, Karim, and Masum started a business by investing Tk.150000, Tk.120000, and Tk.135000 respectively. Find the share of Karim out of the annual profit of Tk. 56700?

Solution:
Ratio of the investments of Rahim, Karim and Masum = 150000 : 120000 : 135000
= 150 : 120 : 135
= 10 : 8 : 9
Sum of the ratio = 10 + 8 + 9
= 27

∴ Karim's share = 56700 × (8/27)
= 16,800 Tk.
৩৯১.
B's income is 60% of A's, and the ratio of their expenditures is 9 : 5. If each saves Tk. 4,000, find A’s income.
  1. ক
    10,000 Taka
  2. খ
    12,000 Taka
  3. গ
    15,000 Taka
  4. ঘ
    40,000 Taka
ব্যাখ্যা

Question: B's income is 60% of A's, and the ratio of their expenditures is 9 : 5. If each saves Tk. 4,000, find A’s income.

Solution:
Suppose,
A's income = 100,
B's income 60% of 100 = 60
A : B = 100 : 60 = 5 : 3

So,
A’s income = 5x, B’s income = 3x
A’s expense = 9y, B’s expense = 5y

Then their savings are:
A’s savings = Income - Expense = 5x - 9y.......(1)
B’s savings = Income - Expense = 3x - 5y........(2)

Given that each saves Tk. 4000:
5x - 9y = 4000
3x - 5y = 4000

Subtract equation (2) from (1):
(5x - 9y) - (3x - 5y) = 0 
 ⇒ 2x - 4y = 0 
⇒ x = 2y

Substitute x = 2y into equation (2):
3(2y) - 5y = 4000
⇒ 6y - 5y = 4000
⇒  y = 4000

Then x = 2y = 8000

Finally, A’s income = 5x = 5 × 8000 = 40,000 Taka

∴ A's income = 40,000 Taka

৩৯২.
Monir started a business investing Tk. 9000. After five months, Amir joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Amir in the profit?
  1. ক
    ক) TK. 2280
  2. খ
    খ) TK. 2520
  3. গ
    গ) TK. 2380
  4. ঘ
    ঘ) TK. 2240
ব্যাখ্যা
Question: Monir started a business investing Tk. 9000. After five months, Amir joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Amir in the profit?

Solution:
Now as per the question,
Monir invested for 12 months
and Amir invested for (12 - 5) = 7 months.

So
Monir : Amir = (9000 × 12) : (8000 × 7)
= 108000 : 56000
= 108 : 56
= 27 : 14

Amir Ratio in profit will be = 6970 × (14/41)
= Tk. 2380
৩৯৩.
A pair of articles was bought for Tk. 35.70 at a discount of 15%. What must be the marked price of each of the articles? 
  1. ক
    ক) Tk. 42
  2. খ
    খ) Tk. 36
  3. গ
    গ) Tk. 21
  4. ঘ
    ঘ) Tk. 18
ব্যাখ্যা
Question: A pair of articles was bought for Tk. 35.70 at a discount of 15%. What must be the marked price of each of the articles? 

Solution: 
Selling price =Tk.  35.70
Discount = 15%.

Let the M.P be 100%.
The selling price will be 100% - 15% = 85%
⇒ 85% = 35.70
⇒ 100% = 35.70 × (100/85)
⇒ 100% = Tk. 42

∴ The Marked price is Tk. 42 .
The marked price of each of the articles = 42/2 = 21Tk. 
৩৯৪.
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
    10 months
  2. খ
    8 months
  3. গ
    6 months
  4. ঘ
    4 months
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 of profit = Tk. 2z/3,
A's share of profit = 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 n months.
Then,
{(X/ 4) × 15}/{(3X/4) × n) = 1/2
⇒ 15/3n = 1/2
⇒ 3n = 30
⇒ n = 10

∴ B's money was used for 10 months.
৩৯৫.
A, B, and C subscribe Tk. 45,000 for a business. A subscribes Tk. 6,000 more than B, and B subscribes Tk. 3,000 more than C. Out of a total profit of Tk. 30,000, how much does A receive?
  1. ক
    12555 Tk
  2. খ
    13333 Tk
  3. গ
    14455 Tk
  4. ঘ
    12666 Tk
ব্যাখ্যা
Example: A, B, and C subscribe Tk. 45,000 for a business. A subscribes Tk. 6,000 more than B, and B subscribes Tk. 3,000 more than C. Out of a total profit of Tk. 30,000, how much does A receive?

Solution:
Let C subscribe x taka.
So, B subscribes x + 3000 taka,
and A subscribes x + 3000 + 6000 = x + 9000 taka.

x + x + 3000 + x + 9000 = 45000
⇒ 3x + 12000 = 45000
⇒ 3x = 33000
⇒ x = 11000 taka

A receives = {(x + 9000)/45000} × 30000
= (20000/45000) × 30000
= 13333.33 taka
≈ 13333 taka
৩৯৬.
Last year, Company X made p dollars in profit. Half of the profit went to the company's founder. The rest was split evenly among his four other partners. In terms of p, how much did each of the other partners receive?
  1. ক
    p/4
  2. খ
    p/6
  3. গ
    2p/5
  4. ঘ
    p/8
ব্যাখ্যা

Question: Last year, Company X made p dollars in profit. Half of the profit went to the company's founder. The rest was split evenly among his four other partners. In terms of p, how much did each of the other partners receive?

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

Half of the profit went to the founder, so the founder received,
1/2 of p = p/2

Remaining Profit = p - p/2 = p/2

The remaining profit was split among 4 partners.
∴ Each partner gets = (p/2) ÷ 4
= (p/2) × (1/4)
= p/8

৩৯৭.
A dealer purchased a washing machine for Tk.7660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.
  1. ক
    ক) 9600 Taka
  2. খ
    খ) 8700 Taka
  3. গ
    গ) 9500 Taka
  4. ঘ
    ঘ) 9575 Taka
ব্যাখ্যা
প্রশ্ন: A dealer purchased a washing machine for Tk.7660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.

সমাধান:
১০% লাভে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১১০ টাকা
∴ ক্রয়মূল্য ৭৬৬০ টাকা হলে বিক্রয়মূল্য (১১০ × ৭৬৬০)/১০০ টাকা
= ৮৪২৬ টাকা

১২% কমিশনে,
বিক্রয়মূল্য ৮৮ টাকা হলে গায়ে লিখা মূল্য ১০০ টাকা 
∴ বিক্রয়মূল্য ৮৪২৬ টাকা হলে গায়ে লিখা মূল্য (১০০ × ৮৪২৬)/৮৮ টাকা 
= ৯৫৭৫ টাকা 
৩৯৮.
A starts a business with Tk. 3800 and after 4 months, B joins with some capital. At the end of the year, the profit is divided in the ratio 3 : 4. What is B's contribution to the business?
  1. ক
    ক) Tk. 8400
  2. খ
    খ) Tk. 9600
  3. গ
    গ) Tk. 7600
  4. ঘ
    ঘ) Tk. 6300
ব্যাখ্যা
Question: A starts a business with Tk. 3800 and after 4 months, B joins with some capital. At the end of the year, the profit is divided in the ratio 3 : 4. What is B's contribution to the business?

Solution: 
Let the Contribution of B is Tk. x
A invested for 12 months and B invested for (12 - 4) = 8 months

Now
⇒ (3800 × 12)/(x × 8) = 3/4
⇒ (3800 × 12 × 4)/(3 × 8)= x
⇒ x = 7600

∴ Contribution of B to the business is 7600
৩৯৯.
The true discount on a bill of Tk. 2700 is Tk. 200. What is the banker's discount?
  1. ক
    Tk. 210
  2. খ
    Tk. 212
  3. গ
    Tk. 216
  4. ঘ
    Tk. 218
ব্যাখ্যা
Question: The true discount on a bill of Tk. 2700 is Tk. 200. What is the banker's discount?

Solution:
Face value = Tk. 2700
TD = Tk. 200
PW (present worth) = FV (face value) - TD (true discount)
= 2700 - 200
= 2500

True discount is the simple interest on the present value for the unexpired time.

Now, simple interest on Tk. 2500 for unexpired time = Tk. 200
The rate of simple interest = (200/2500) × 100% = 8%

Banker's discount is the simple interest on the face value of the bill for unexpired time.

simple interest on Tk. 2700 for unexpired time or remaining time.
R = 8%
Banker's discount = 2700 × (8/100) = 216
৪০০.
Three partners X, Y, and Z invest Tk. 60,000 in a business. X invests Tk. 8,000 more than Y, and Y invests Tk. 5,000 more than Z. If the total profit is Tk. 36,000, how much does X receive?
  1. ক
    Tk.18200
  2. খ
    Tk.16200
  3. গ
    Tk.14570
  4. ঘ
    Tk.15820
  5. ঙ
    None of these
ব্যাখ্যা
Question: Three partners X, Y, and Z invest Tk. 60,000 in a business. X invests Tk. 8,000 more than Y, and Y invests Tk. 5,000 more than Z. If the total profit is Tk. 36,000, how much does X receive?

Solution:
Let Z's investment be Tk. x.
Y invests Tk. 5,000 more than Z, so Y's investment = Tk. (x + 5,000)
X invests Tk. 8,000 more than Y, so X's investment = Tk. (x + 5,000 + 8,000) = Tk. (x + 13,000)

Since the total investment is Tk. 60000,
⇒ X + Y + Z = 60000
⇒ (x + 13000) + (x + 5000) + x = 60000
⇒ 3x + 18000 = 60000
⇒ 3x = 42000
⇒ x = 14000

So,
Z's investment = Tk. 14,000
Y's investment = Tk. (14,000 + 5,000) = Tk. 19,000
X's investment = Tk. (19,000 + 8,000) = Tk. 27,000

Given that, Total profit = Tk. 36,000

X receive = (X’s Investment​/Total Investment) × Total Profit
= (27000/60000) × 36000
= (27/60) × 36000
= 27 × 600
= 16200

∴ X receives Tk. 16,200 from the profit.