Partnership and Discount

PrepBank · পাতা ২ / ৫ · ১০১–২০০ / ৪৪৪

১০১.

A laptop is marked at a price 20% above its cost price. At what discount it should be sold to make a 5% profit?

ক
ক) 14.5%
খ
খ) 12.5%
গ
গ) 10.5%
ঘ
ঘ) 15.0%

ব্যাখ্যা

Let
Cost price of product be Tk. 100
Marked price = (100 + 20)% of 100
= 120
Profit = 5%
⇒ Selling price = (100 + 5)% of 100
= 105

⇒ Discount = Marked price - Selling price
= 120 - 105
= 15
⇒ Discount %= (15/120) × 100
= 12.5%

∴ 12.5% is discount should be sold so as to make 5% profit.

১০২.

A, B and C entered into a partnership and their share are in the ratio of 1/2 : 1/3 : 1/4. After 2 months, A withdraw half of his capital and after another 10 months a profit of Tk. 378 is divided among them. What is B’s share after 12 months?

ক
ক) Tk. 124
খ
খ) Tk. 144
গ
গ) Tk. 154
ঘ
ঘ) Tk. 114

ব্যাখ্যা

Ratio of initial investment of A, B and C = 1/2 : 1/3 : 1/4 = 6 : 4 : 3

Let A’s initial investment is = 6x
Let B’s initial investment is = 4x
Let C’s initial investment is = 3x

∴ A : B : C = (6x × 2 + 3x × 10) : (4x × 12) : (3x × 12)
⇒ (42x) : (48x) : (36x)
⇒ 42 : 48 : 36
⇒ 7 : 8 : 6

∴ B’s share in the profit = 378 × (8/21)
⇒ Tk. 144

১০৩.

P starts a business with Tk 6000 and after 3 months, Q joins with P as his partner. After a year, the profit is divided in the ratio 4 : 5. What is Q's contribution in the capital?

ক
80000 tk
খ
9000 tk
গ
10000 tk
ঘ
None of the above

ব্যাখ্যা

Question: P starts a business with Tk 6000 and after 3 months, Q joins with P as his partner. After a year, the profit is divided in the ratio 4 : 5. What is Q's contribution in the capital?

Solution:
Let Q's capital be Tk x
∴ P's share in 12 months = 6000 × 12
And, Q's share in 9 months = 9x
Then,
(6000 × 12)/(9x) = 4/5
⇒ 72000/9x = 4/5
⇒ 72000 = 36x/5
⇒ 72000 × 5 = 36x
⇒ 360000 = 36x
⇒ x = 10000

১০৪.

The business was started by A, B, and C with investments of Tk.150000, Tk.120000, and Tk.135000. What is B’s portion of the total annual profit of Tk. 56700?

ক
Tk. 16,800
খ
Tk. 14,720
গ
Tk. 18,480
ঘ
Tk. 28,652

ব্যাখ্যা

Question: The business was started by A, B, and C with investments of Tk.150000, Tk.120000, and Tk.135000. What is B’s portion of the total annual profit of Tk. 56700?

Solution:
The ratio of the investments of A, B and C = 150000 : 120000 : 135000
= 150 : 120 : 135
= 10 : 8 : 9

Sum of the ratio = 10 + 8 + 9
= 27

∴ B's share = 56700 × (8/27)
= 16,800 Tk.

১০৫.

Mijan,Jewel, and Tasif rent a pasture. Mijan puts 10 oxen for 7 months, Jewel puts 12 oxen for 5 months and Tasif puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 1750, how much must Tasif pay as his share of rent?

ক
ক) Tk. 700
খ
খ) Tk. 600
গ
গ) Tk. 450
ঘ
ঘ) Tk. 900

ব্যাখ্যা

প্রশ্ন: Mijan,Jewel, and Tasif rent a pasture. Mijan puts 10 oxen for 7 months, Jewel puts 12 oxen for 5 months and Tasif puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 1750, how much must Tasif pay as his share of rent?

সমাধান:
Mijan : Jewel : Tasif = (10 × 7) : (12 × 5) : (15 × 3)
= 70 : 60 : 45
= 14 : 12 : 9

∴ Tasif's share of rent = 1750 × (9/35) = 450.

১০৬.

The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 28. Find the present worth.

ক
600
খ
670
গ
700
ঘ
740

ব্যাখ্যা

Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 28. Find the present worth.

Solution:
Banker Gain = 28
True Discount = (Bnakers gain × 100)/(rate × time) = (28 × 100)/(10 × 2) = 140

Banker's Gain = Banker's Discount - True discount
⇒ 28 = Banker's discount - 140
∴ Banker's discount = 140 + 28 = 168

Now, banker's discount is the interest on the face value
Let the face value = x
So,
x × (10/100) × 2 = 168
⇒ x × 0.1 × 2 = 168
⇒ x = 168/0.2 = 840

Now,
Present Worth = Face value - True discount
= 840 - 140
= 700

১০৭.

A sum of tk. 558 is to be divided among A, B and C such that 2 times A's share, 3 times B's share and 5 times C's share are all equal. The share of C is

ক
135
খ
122
গ
108
ঘ
102

ব্যাখ্যা

Question: A sum of tk. 558 is to be divided among A, B and C such that 2 times A's share, 3 times B's share and 5 times C's share are all equal. The share of C is

Solution:
Let,
2A = 3B = 5C = x
∴ A = x/2 , B = x/3 , C = x/5

A : B : C = x/2 : x/3 : x/5
To eliminate the fractions, find the LCM of 2, 3, and 5, which is 30.

Multiply each term by 30 to get:
A : B : C = 30x/2 : 30x/3 : 30x/5
= 15x : 10x : 6x

So, the ratio of A : B : C is = 15 : 10 : 6.

The total parts = (15 + 10 + 6) = 31 parts.

The share of C is = (558 × 6)/31
= 108

১০৮.

To attract more visitors, the zoo authorities announced a 20% discount on each ticket, the original price of which was 25 paisa. As a result, the total ticket-sale revenue increased by 36%. What is the percentage increase in the number of visitors?

ক
40%
খ
60%
গ
70%
ঘ
No change

ব্যাখ্যা

Question: To attract more visitors, the zoo authorities announced a 20% discount on each ticket, the original price of which was 25 paisa. As a result, the total ticket-sale revenue increased by 36%. What is the percentage increase in the number of visitors?

Solution:
Let the number of visitors in the beginning = 100

Original ticket price = 25 paisa = 0.25 Tk
∴ Total original revenue = 0.25 × 100
= 25 Tk

At 20% discount on every ticket,
New ticket price = 25 × (80/100)
= 20 paisa
= 0.20 Tk

Sale increased by 36%
∴ New revenue = 25 × (136/100)
= 34 Tk

Number of visitors now = New revenue/New ticket price
= 34/0.20
= 34/(20/100)
= 34 × 5
= 170

∴ Percentage increase in number of visitors = [(170 − 100)/100] × 100
= (70 × 100)/100
= 70%

১০৯.

Successive discount of 20% and 15% are equal to a single discount of-

ক
30%
খ
32%
গ
34%
ঘ
35%

ব্যাখ্যা

Question: Successive discount of 20% and 15% are equal to a single discount of-

Solution:
Let, The original price be 100 tk

After a 20% discount, the price is = 100 - 20 = 80 tk
Again, after a 15% discount, the new price is = 80 - {80 × (15/100)}
= 80 - 12
= 68

∴ Total discount= (100 - 68) = 32%

১১০.

A started a business with Tk. 4000 and is joined afterwards by B with Tk. 6000. After how many months did B join if the profits at the end of the year are divided equally?

ক
3 months
খ
4 months
গ
5 months
ঘ
6 months

ব্যাখ্যা

Question: A started a business with Tk. 4000 and is joined afterwards by B with Tk. 6000. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Let,
B joined after = x months

Then,
4000 × 12 = 6000 × (12 - x)
⇒ 48000 = 72000 - 6000x
⇒ 480 = 720 - 60x
⇒ 60x = 240
∴ x = 4

∴ B joined after 4 months.

১১১.

A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

ক
ক) 4 months.
খ
খ) 5 months.
গ
গ) 6 months.
ঘ
ঘ) 7 months.

ব্যাখ্যা

Question: A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Suppose,
B joined after x months.

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

∴ B joined after 5 months.

১১২.

A sum of Tk. 6400 is divided among three workers in the ratio 3/5 : 2 : 5/3. The share of the second worker is-

ক
ক) Tk. 900
খ
খ) Tk. 2500
গ
গ) Tk. 3000
ঘ
ঘ) Tk. 3600

ব্যাখ্যা

Question: A sum of Tk. 6400 is divided among three workers in the ratio 3/5 : 2 : 5/3. The share of the second worker is-

Solution:
ratio of share = 3/5 : 2 : 5/3
= 9 : 30 : 25
The share of the second worker is = 6400 × (30/64) = Tk. 3000

১১৩.

Shakil and Rony invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Shakil invested Tk. 40000, then what was the amount invested by Rony?

ক
ক) Tk. 30000
খ
খ) Tk. 45000
গ
গ) Tk. 60000
ঘ
ঘ) Tk. 75000

ব্যাখ্যা

Question: Shakil and Rony invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Shakil invested Tk. 40000, then what was the amount invested by Rony?

Solution:
Given ratio = 2 : 3
Let,
Shakil invested 2x Taka
Rony invested 3x Taka

ATQ,
2x = 40000
∴ x = 20000

∴ Rony invested 3x Taka = 3 × 20000 Taka
= 60000 Taka

১১৪.

In a business partnership, Ajay and Vijay invested Tk. (1400 + x) and Tk. (1800 + 2x). After 12 months, Vijay’s profit amounted to Tk. 3200 out of a total Tk. 5600. Calculate Ajay’s starting investment.

ক
Tk.1500
খ
Tk.2000
গ
Tk.1800
ঘ
Tk.1600
ঙ
Tk.2020

ব্যাখ্যা

Question: In a business partnership, Ajay and Vijay invested Tk. (1400 + x) and Tk. (1800 + 2x). After 12 months, Vijay’s profit amounted to Tk. 3200 out of a total Tk. 5600. Calculate Ajay’s starting investment.

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

১১৫.

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?

ক
3 months
খ
6 months
গ
10 months
ঘ
12 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.

১১৬.

P, Q, and R opened a shop together. P invests four times as much as Q, and Q invests one-fifth as much as R. After one year, the total profit is Tk 18,000. What is Q's share of the profit?

ক
Tk 1500
খ
Tk 1800
গ
Tk 2000
ঘ
Tk 2400

ব্যাখ্যা

Question: P, Q, and R opened a shop together. P invests four times as much as Q, and Q invests one-fifth as much as R. After one year, the total profit is Tk 18,000. What is Q's share of the profit?

Solution:
Let R's investment = x taka
Then Q's investment = 1/5 of x = x/5
And P's investment = 4 × (x/5) = 4x/5

So the ratio of investments (or profit) is:
P : Q : R
= 4x/5 : x/5 : x
= 4 : 1 : 5

Total ratio = 4 + 1 + 5 = 10

Total profit = Tk 18,000

∴ Q's share = (1/10) × 18000 = Tk 1800

১১৭.

Three partners A, B, and C invest Tk. 60000 in a business. A invests Tk. 8000 more than B, and B invests Tk. 5000 more than C. If the total profit is Tk. 30000, how much does A receive?

ক
Tk. 14200
খ
Tk. 13500
গ
Tk. 10500
ঘ
Tk. 15600
ঙ
None of these

ব্যাখ্যা

Question: Three partners A, B, and C invest Tk. 60000 in a business. A invests Tk. 8000 more than B, and B invests Tk. 5000 more than C. If the total profit is Tk. 30000, how much does A receive?

Solution:
Let C's investment be Tk. x.
B invests Tk. 5000 more than C, so B's investment = Tk. (x + 5000)
A invests Tk. 8000 more than B, so A's investment = Tk. (x + 5000 + 8000) = Tk. (x + 13000)

Since the total investment is Tk. 60000,
⇒ A + B + C = 60000
⇒ (x + 13000) + (x + 5000) + x = 60000
⇒ 3x + 18000 = 60000
⇒ 3x = 42000
⇒ x = 14000

So,
C's investment = Tk. 14000
B's investment = Tk. (14000 + 5000) = Tk. 19000
A's investment = Tk. (19000 + 8000) = Tk. 27000

Given that, Total profit = Tk. 30000

A receive = (A’s Investment/Total Investment) × Total Profit
= (27000/60000) × 30000
= (27/60) × 30000
= 27 × 500
= 13500

∴ A receives Tk. 13500 from the profit.

১১৮.

The original cost of a machine is Tk. 10,000. If the annual depreciation is 10%, after how many years will it be valued at Tk. 6,561?

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6
ঙ
ঙ) 7

ব্যাখ্যা

Cost of machine 10000/-
Depreciation 10% each year.
1st year = 10000 - 1000 = 9000/-
2nd year = 9000 - 900 = 8100/-
3rs year = 8100 - 810 = 7290/-
4th year = 7290 - 729 = 6561/-
Depreciation will be deducted from the amount left after subtracting previous depreciation value.

১১৯.

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

ক
11 : 5
খ
12 : 7
গ
15 : 2
ঘ
17 : 3

ব্যাখ্যা

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

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

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

১২০.

Having incurred a 16% loss on a saree sold for Tk. 3360, a shopkeeper now wishes to set a marked price that allows for a 15% profit, even after applying an 8% discount. What is that price?

ক
Tk. 3000
খ
Tk. 4500
গ
Tk. 3500
ঘ
Tk. 5000

ব্যাখ্যা

Question: Having incurred a 16% loss on a saree sold for Tk. 3360, a shopkeeper now wishes to set a marked price that allows for a 15% profit, even after applying an 8% discount. What is that price?

Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.

Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000

15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600

discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000

১২১.

Rina and Shila entered into a partnership with their capitals in the ratio 5 : 6 At the end of 8 months, Rina withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Shila's capital was used?

ক
ক) 12 months
খ
খ) 14 months
গ
গ) 16 months
ঘ
ঘ) 18 months

ব্যাখ্যা

Question: Rina and Shila entered into a partnership with their capitals in the ratio 5 : 6 At the end of 8 months, Rina withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Shila's capital was used?

Solution:
Shila মূলধন x সময়ের জন্য খেটেছিলো

প্রশ্নমতে,
(5 × 8)/(6 × x) = 5/9
30x = 360
x = 360/30
x = 12

১২২.

Nila and Nipa entered into a partnership with their capitals in the ratio 5 : 6 At the end of 8 months, Nila withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Nipa's capital was used?

ক
ক) 8 months
খ
খ) 12 months
গ
গ) 10 months
ঘ
ঘ) 14 months

ব্যাখ্যা

Question: Nila and Nipa entered into a partnership with their capitals in the ratio 5 : 6 At the end of 8 months, Nila withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long Nipa's capital was used?

Solution:
Nipa মূলধন x সময়ের জন্য খেটেছিলো

প্রশ্নমতে,
(5 × 8)/(6 × x) = 5/9
30x = 360
x = 360/30
x = 12

১২৩.

In a business Titu invested twice as Rasel for a year. The total amount is 21000. After one year Titu received a total of 17000 Taka. What is Rasel's profit?

ক
ক) 8500 Tk
খ
খ) 1500 Tk
গ
গ) 1850 Tk
ঘ
ঘ) 1000 tk

ব্যাখ্যা

Question: In a business Titu invested twice as Rasel for a year. The total amount is 21000. After one year Titu received a total of 17000 Taka. What is Rasel's profit?

Solution:
ধরি, রাসেলের বিনিয়োগ = ক টাকা
টিটুর বিনিয়োগ = ২ক টাকা
প্রশ্নমতে,
৩ক = ২১০০০
ক = ৭০০০ টাকা
∴ টিটুর বিনিয়োগ = ১৪০০০ টাকা
টিটুর লাভ = ১৭০০০ - ১৪০০০ = ৩০০০ টাকা

১৪০০০ টাকায় লাভ হয় ৩০০০ টাকা
৭০০০ টাকায় লাভ হয় = ৩০০০/২ = ১৫০০ টাকা

∴ রাসেলের লাভ হবে ১৫০০ টাকা।

১২৪.

The price of a house is decreased from Fifteen lakhs taka to Twelve lakhs taka. Find the percentage of decrease.

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: The price of a house is decreased from Fifteen lakhs taka to Twelve lakhs taka. Find the percentage of decrease.

Solution:

Original price = Tk. 15,00,000

Changed price = Tk. 12,00,000

∴ Decrease in price = 15,00,000 - 12,00,000 = Tk. 3,00,000

Therefore, the percentage of decrease = (3,00,000)/(15,00,000) × 100 % = 20%.

১২৫.

Tamim and Shakib invest Tk. 15,000 and Tk. 25,000 respectively. Tamim, being the active partner, gets 10% of the total profit as salary. If the annual profit is Tk. 10,000, find Tamim’s total earnings.

ক
4,200 Taka
খ
4,375 Taka
গ
4,575 Taka
ঘ
4,775 Taka

ব্যাখ্যা

Question: Tamim and Shakib invest Tk. 15,000 and Tk. 25,000 respectively. Tamim, being the active partner, gets 10% of the total profit as salary. If the annual profit is Tk. 10,000, find Tamim’s total earnings.

Solution:
Total profit = 10,000 Taka.
Tamim gets 10% of total profit as salary.
Tamim’s salary = 10% of 10,000
= (10/100) × 10,000
= 1,000 Taka.

Remaining profit after salary = 10,000 - 1,000
= 9,000 Taka.

Divide remaining profit in ratio of their capitals
Tamim : Shakib = 15,000 : 25,000
= 3 : 5

Tamim’s share = [3/(3 + 5)] × 9,000
= [3/8] × 9,000
= 3,375 Taka

Tamim’s total earning = Tamim’s salary + Tamim’s profit share
= 1,000 + 3,375
= 4,375 Taka

∴ Tamim's total earning = 4,375 Taka

১২৬.

Rimi bought a mobile phone at a discount of 20%. Had the discount received was 25%, she would have saved Tk 2,000 more. How much did she pay (in Tk) for the mobile phone?

ক
ক) 32,000
খ
খ) 24,000
গ
গ) 18,000
ঘ
ঘ) 36,000

ব্যাখ্যা

Question : Rimi bought a mobile phone at a discount of 20%. Had the discount received was 25%, she would have saved Tk 2,000 more. How much did she pay (in Tk) for the mobile phone?

Solution:

Let the actual price of the phone be 100x

Cost price of Rimi = 100x × (100 - 20)%
⇒ 100x × 80%
⇒ 80x

If 25% discount is given then,
Cost price of Rimi = 100x × (100 - 25)%
⇒ 75x

According to the question,
80x - 75x = 2000
⇒ 5x = 2000
⇒ x = 400

So, actual cost price of Rimi = 80 × 400
⇒ 32000

∴ She paid 32000 (in Tk) for the mobile phone.

১২৭.

Two friends invested Tk.1500 and Tk. 2500 in a business. They earned a profit of Tk. 800. 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?

ক
Tk. 350 and Tk. 450
খ
Tk. 360 and Tk. 500
গ
Tk. 420 and Tk. 550
ঘ
Tk. 280 and Tk. 325

ব্যাখ্যা

Question: Two friends invested Tk.1500 and Tk. 2500 in a business. They earned a profit of Tk. 800. 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 : 2500
= 3 : 5

∴ Share of first friend = Tk. [(400/2) + {400 × (3/8)}]
= Tk. (200 + 150)
= Tk. 350

∴ Share of second friend = Tk. [(400/2) + {400 × (5/8)}]
= Tk. (200 + 250)
= Tk. 450

১২৮.

Yesterday, a bookstore had Tk. 3,600 in total sales. If 1/4 of the total sales were from the sale of books that had been reduced by 25 percent, what would have been the total sales yesterday if all of the books had been sold at full price?

ক
Tk. 3,700
খ
Tk. 3,900
গ
Tk. 4,000
ঘ
Tk. 4,200

ব্যাখ্যা

Question: Yesterday, a bookstore had Tk. 3,600 in total sales. If 1/4 of the total sales were from the sale of books that had been reduced by 25 percent, what would have been the total sales yesterday if all of the books had been sold at full price?

Solution:
মোট বিক্রয় = Tk. 3,600

ডিসকাউন্ট দেওয়া বইয়ের বিক্রয়:
= Tk. 3,600 × (1/4)
= Tk. 900

এই Tk. 900 এসেছে 25% ছাড়ের পরে বিক্রি থেকে, অর্থাৎ এটি আসল মূল্যের 75%।
∴ আসল মূল্য = 900 ÷ 0.75 = Tk. 1,200

বাকি বই পূর্ণ দামে বিক্রি হয়েছে:
= মোট বিক্রি - ডিসকাউন্ট বই বিক্রি
= Tk. 3,600 - Tk. 900
= Tk. 2,700

∴ সব বই পূর্ণ দামে বিক্রি হলে মোট বিক্রয় হতো:
= Tk. 1,200 + Tk. 2,700
= Tk. 3,900

১২৯.

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-

ক
ক) Tk. 10
খ
খ) Tk. 12
গ
গ) Tk. 15
ঘ
ঘ) Tk. 20

ব্যাখ্যা

Question: 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-

Solution:
Dividend on Tk. 20 = Tk. (9/100) × 20)
= Tk 9/5

Tk.12 is an income on Tk.100.
∴ Tk. 9/5 is an income on = Tk. (100/12 × 95)
= Tk.15

১৩০.

A and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit?

ক
310
খ
350
গ
370
ঘ
330

ব্যাখ্যা

Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respectively.
Ratio in which profit will be divided
According to the question,
= (4x × 3) + {3/4 × (4x × 7)} : (5x × 3) + {4/5 × (5x × 7)}
= (12 + 21) : (15 + 28)
= 33 : 43
A's share = 760 × (33/76)
= 330.

১৩১.

Tk 20 is the true discount on Tk 260 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?

ক
ক) Tk. 10
খ
খ) Tk. 10.40
গ
গ) Tk. 15.20
ঘ
ঘ) Tk. 13

ব্যাখ্যা

Simple Interest on Tk. (260 - 20) for a given time = Tk. 20
Simple Interest on Tk. 240 for half the time = Tk. 10
True Discount On Tk. 250 = Tk. 10.
∴ True Discount On Tk. 260 = Tk. {(10/250) × 260}
= Tk. 10.40

১৩২.

A clothing store offers a dress initially at Tk. 1000. 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?

ক
600
খ
680
গ
660
ঘ
690

ব্যাখ্যা

Question: A clothing store offers a dress initially at Tk. 1000. 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 1000(1 - 0.15) = 1000(0.85) = 850
So the dress is worth Tk. 850

After the second discount,
we have 850(1 - 0.20) = 850(0.8) = 680

So the final dress price is Tk. 680

১৩৩.

Two persons Choton and Billal started a business in which Choton invested Tk. 50000, Billal invested Tk. 80000, after 4 months Robiul joined them with a certain amount. At the end of the year, a total profit of Tk. 40000 was recorded. Robiul's share in the profit was Tk. 15000, then find Robiul's investment in the business.

ক
Tk. 113000
খ
Tk. 117000
গ
Tk. 120000
ঘ
Tk. 121000

ব্যাখ্যা

Question: Two persons Choton and Billal started a business in which Choton invested Tk. 50000, Billal invested Tk. 80000, after 4 months Robiul joined them with a certain amount. At the end of the year, a total profit of Tk. 40000 was recorded. Robiul's share in the profit was Tk. 15000, then find Robiul's investment in the business.

Solution:
Let,
Robiul's investment in the business be Tk. 1000x
Profit ratio of Choton, Billal and Robiul = (50000 × 12) : (80000 × 12) : {1000x × (12 - 4)}
= 75 : 120 : x

Total profit = 75 + 120 + x = 195 + x

Robiul's share in profit = x
ATQ,
(195 + x)/x = 40000/15000
⇒ (195 + x)/x = 8/3
⇒ 3(195 + x) = 8x
⇒ 585 + 3x = 8x
⇒ 5x = 585
⇒ x = 117

Investment by Robiul = 1000 × 117 = Tk. 117000

১৩৪.

A, B, C enter into a partnership investing Tk. 35,000 and Tk. 45,000 and Tk. 55,000 respectively. Total profit of A, B, C, at Tk. 44,550. So B's profit is-

ক
Tk. 18,150
খ
Tk. 14,850
গ
Tk. 11,550
ঘ
Tk. 14,750

ব্যাখ্যা

Question: A, B, C enter into a partnership investing Tk. 35,000 and Tk. 45,000 and Tk. 55,000 respectively. Total profit of A, B, C, at Tk. 44,550. So B's profit is-

Solution:
A : B : C = 35000 : 45000 : 55000
A : B : C = 35 : 45 : 55

∴ Sum of the ratio = 35 + 45 + 55 = 135

∴ B's profit is = 44550 × (45/135)
= 14850

∴ B's profit is Tk. 14,850.

১৩৫.

A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?

ক
ক) 15%
খ
খ) 10%
গ
গ) 5%
ঘ
ঘ) 25%

ব্যাখ্যা

প্রশ্ন: A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?

সমাধান:
ধরি,
দ্রব্যটির আসল মূল্য ক টাকা

৪০% দাম বাড়িয়ে ধরলে দাম হয় = ক + (ক × ৪০)/১০০ টাকা
= ১.৪ক টাকা

২৫% কমিশন দিলে দাম হয় = ১.৪ক - (১.৪ক × ২৫)/১০০ টাকা
= ১.৪ক - ০.৩৫ক টাকা
= ১.০৫ক টাকা

লাভ = ১.০৫ক - ক টাকা
= ০.০৫ক টাকা

ক টাকায় লাভ হয় = ০.০৫ক টাকা
∴ ১ টাকায় লাভ হয় = ০.০৫ক/ক = ০.০৫ টাকা
∴ ১০০ টাকায় লাভ হয় = (০.০৫ × ১০০) টাকা
= ৫ টাকা

১৩৬.

The true discount on a bill of Tk. 540 is Tk. 90. The banker's discount is:

ক
ক) 60
খ
খ) 108
গ
গ) 110
ঘ
ঘ) 112

ব্যাখ্যা

P.W. = Tk.(540−90) = Tk.450
∴S.I. on Tk.450
= Tk. 90
S.I.on Tk. 540
= Tk.(90/450×540)
= Tk.108
∴B.D.= Tk.108

১৩৭.

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

ক
ক) Tk. 14,700
খ
খ) Tk. 1,900
গ
গ) Tk. 13,600
ঘ
ঘ) Tk. 8,400

ব্যাখ্যা

Let C subscribes Tk. y.
Therefore, B subscribes Tk. (y + 5000)
and A subscribes Tk. (y + 5000 + 4000) or Tk. (y + 9000)

y + y + 5000 + y + 9000 = 50,000
3y + 14,000 = 50,000
3y = 36,000
y = 12,000

The ratio of investment of A, B and C = (12,000 + 9,000) : (12,000 + 5000) : 12,000
= 21,000 : 17,000 : 12,000
= 21: 17 : 12

Therefore, A receives=( 21 × 35,000)/(21 + 17 + 12)
= Tk. 14,700

১৩৮.

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, A receives-

ক
Tk. 8400
খ
Tk. 11,900
গ
Tk. 13,600
ঘ
Tk. 14,700

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. 35,000, A receives-

Solution:
Let C = 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.

A's share = 35000 × (21/50) = Tk. 14,700.

১৩৯.

Junayed starts a business with TK 9000 and after one year, Rayhan joins with junayed by investing a certain amount. At the end of 2 years, If 3 : 2 is the proportion of the profit then Rayhan's contribution to the capital is-

ক
12000 TK
খ
15000 TK
গ
18000 TK
ঘ
16000 TK

ব্যাখ্যা

Question: Junayed starts a business with TK 9000 and after one year, Rayhan joins with junayed by investing a certain amount. At the end of 2 years, If 3 : 2 is the proportion of the profit then Rayhan's contribution to the capital is-

Solution:
Let,
Rayhan's capital be TK P
Junayed's investment = TK 9000 for 24 months
Rayhan's investment = TK p for 12 months
we know that, profit ratio = investing ratio

ATQ,
(9000 × 24)/(p × 12) = 3 : 2
or, (9000 × 24) : 12p = 3 : 2
or, (9000 × 24)/12p = 3/2
or, 36p = (2 × 24 × 9000)
or, p = (48 × 9000)/36
∴ p = 12000

The required answer is 12000 TK

১৪০.

A shirt is being sold for Tk. 1350 after a 10% discount. Determine its original price.

ক
Tk. 1400
খ
Tk. 1450
গ
Tk. 1500
ঘ
Tk. 1550

ব্যাখ্যা

Question: A shirt is being sold for Tk. 1350 after a 10% discount. Determine its original price.

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

Discount = 10% of x
= 10x/100
= x/10

∴ Selling Price = Original Price - Discount
= x - (x/10)
= 9x/10

Now,
9x/10 = 1350
⇒ 9x = 1350 × 10
⇒ 9x = 13500
⇒ x = 13500/9
∴ x = 1500

∴ Original price = 1500 Tk.

১৪১.

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?

ক
12
খ
16
গ
18
ঘ
22

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

১৪২.

Rina and Shila started a business by investing Tk. 85,000 and Tk. 15,000 respectively. If the business runs for 2 years, what will be the ratio of profit earned by Rina and Shila?

ক
17 : 3
খ
16 : 3
গ
27 : 3
ঘ
13 : 3

ব্যাখ্যা

Question: Rina and Shila started a business by investing Tk. 85,000 and Tk. 15,000 respectively. If the business runs for 2 years, what will be the ratio of profit earned by Rina and Shila?

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

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

১৪৩.

If 7% more is gained by selling a phone for Tk. 25000 then by selling it for Tk. 23600. The cost of the phone is?

ক
Tk. 19000
খ
Tk. 20000
গ
Tk. 21000
ঘ
Tk. 21500

ব্যাখ্যা

Question: If 7% more is gained by selling a phone for Tk. 25000 then by selling it for Tk. 23600. The cost of the phone is?

Solution:
Given,
1st selling price = Tk. 25000
2nd selling price = Tk. 23600

∴ Selling price more = (25000 - 23600) = Tk. 1400

If tk. 7 more gained then the cost price Tk. 100
If tk. 1 more gained then the cost price Tk. (100/7)
If tk.1400 more gained then the cost price Tk. {(100 × 1400)/7}
= Tk. 20000

১৪৪.

A working partner receives a commission equal to 30% of the profit remaining after paying his commission. If his commission is Tk 12,000, find the total profit.

ক
50,000 TK
খ
62,000 TK
গ
52,000 TK
ঘ
60,000 TK

ব্যাখ্যা

Question: A working partner receives a commission equal to 30% of the profit remaining after paying his commission. If his commission is Tk 12,000, find the total profit.

Solution:
Let,
the total profit be K taka
According to the question,
remaining profit after paying 30% working partners commission = (K - 12000)

∴ (K - 12000) × (30/100) = 12000
⇒ (K - 12000) = 12000 × (100/30)
⇒ (K - 12000) = 40,000
⇒ K = 40,000 + 12,000
∴ K = 52,000

so, Total profit = 52,000 TK

১৪৫.

An agent sells goods worth Tk. 22000. If his commission rate was 15.5%, what was the amount of his commission?

ক
3410
খ
2820
গ
3550
ঘ
3230

ব্যাখ্যা

Question: An agent sells goods worth Tk. 22000. If his commission rate was 15.5%, what was the amount of his commission?

Solution:
Commission = 15.5% of 22000
= (155/10) × (1/100) × 22000
= (155/1000) × 22000
= 3410

১৪৬.

The bankers discount and true discount on a sum of money due 8 months hence are Tk.120 & Tk.110 resp. Find the sum.

ক
ক) 1457
খ
খ) 1320
গ
গ) 1140
ঘ
ঘ) 1260

ব্যাখ্যা

Sum = (B.D.×T.D.)/(B.D.−T.D.)
= (120×110) / (120−110)
= 1320

১৪৭.

What is the rate of discount is a car that had a regular price of Tk. 30,00,000 is sold for Tk.27,90,000?

ক
ক) 7%
খ
খ) 8%
গ
গ) 9%
ঘ
ঘ) 10%

ব্যাখ্যা

লিখিতমূল্য = 30,00,000 টাকা
বিক্রয় মূল্য = 27,90,000 টাকা

ছাড় = (30,00,000 - 27,90,000) টাকা
= 2,10,000 টাকা
ছাড়ের হার = {(2,10,000/30,00,000) × 100}%
=7%

১৪৮.

Rafi and Nabil started a business. Rafi invested Tk. 15,000 for 12 months, while Nabil invested Tk. 10,000 for 6 months. After 6 months, Nabil added another Tk. 5,000. If the total profit is Tk. 11,000, what is Nabil’s share of the profit?

ক
Tk 2,000
খ
Tk 3,000
গ
Tk 4,000
ঘ
Tk 5,000

ব্যাখ্যা

Question: Rafi and Nabil started a business. Rafi invested Tk. 15,000 for 12 months, while Nabil invested Tk. 10,000 for 6 months. After 6 months, Nabil added another Tk. 5,000. If the total profit is Tk. 11,000, what is Nabil’s share of the profit?

Solution:
Rafi's share 15,000 × 12 = 180,000
Nabil's share (10,000 × 6) + (15,000 × 6)
= 60,000 + 90,000
= 150,000

Ratio of Rafi : Nabil = 180,000 : 150,000 = 6 : 5

∴ Nabil's profit = (5/11) × 11,000
= Tk 5,000

১৪৯.

A, B and C started a business with initial investments of Tk. 1250, Tk. 1750 and Tk. 2000 respectively. After one year A, B and C made additional investments of Tk. x + 650, Tk. x +500, Tk. x + 850 respectively. Find the profit share of B out of the total profit of Tk. 4350, after two years.

ক
Tk. 1350
খ
Tk. 1450
গ
Tk. 1550
ঘ
Can’t be determined

ব্যাখ্যা

Question: A, B and C started a business with initial investments of Tk. 1250, Tk. 1750 and Tk. 2000 respectively. After one year A, B and C made additional investments of Tk. x + 650, Tk. x +500, Tk. x + 850 respectively. Find the profit share of B out of the total profit of Tk. 4350, after two years.

Solution:
A : B : C = {(1250 × 24) + (x + 650) × 12} : {(1750 × 24) + (x +500) × 12} : {(2000 × 24) + (x + 850) × 12}
= (30000 + 7800 + 12x) : (42000 + 6000 + 12x) : (48000 + 10200 + 12x)
= (37800 + 12x) : (48000 + 12x) : (58200 + 12x)
= {12(3150 + x)} : {12(4000 + x)} : {12(4850 + x)}
= (3150 + x) : (4000 + x) : (4850 + x)

Here x is not defined so the share of B can’t be determined.

১৫০.

Rifat, Joy, Banik subscribe to Tk. 50,000 for a business. Rifat subscribes Tk. 4000 more than Joy and Joy subscribes Tk. 5000 more than Banik. Out of a total profit of Tk. 35000, Rifat receives-

ক
ক) Tk. 8400
খ
খ) Tk. 11900
গ
গ) Tk. 15200
ঘ
ঘ) Tk. 14700

ব্যাখ্যা

প্রশ্ন: Rifat, Joy, Banik subscribe to Tk. 50000 for a business. Rifat subscribes Tk. 4000 more than Joy and Joy subscribes Tk. 5000 more than Banik. Out of a total profit of Tk. 35000, Rifat receives-

সমাধান:
Let,
Banik subscribes = x
Then,
Joy subscribe = x + 5000
Rifat subscribe = x + 5000 + 4000 = x + 9000
∴ x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000

Rifat : Joy : Banik = 21000 : 17000 : 12000
= 21 : 17 : 12

∴ Rifat’s share of profit = 35000 × (21/50) = 14700

১৫১.

In a business venture, Humayun and Kabir contribute in the ratio of 5:4. With 10% of the total profit allocated to charity and Humayun’s share being Tk 945, what is the overall profit?

ক
1720 tk
খ
1800 tk
গ
1890 tk
ঘ
1960 tk

ব্যাখ্যা

Question: In a business venture, Humayun and Kabir contribute in the ratio of 5:4. With 10% of the total profit allocated to charity and Humayun’s share being Tk 945, what is the overall profit?

Solution:
Let,
The total profit = 100 tk

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

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

So, the total profit is 1890 tk.

১৫২.

Sima started a software business by investing Tk. 50,000. After six months, Rajon joined her with a capital of Tk. 80000. After 3 years, they earned a profit of Tk. Tk. 24500. What was Sima’s share in the profit?

ক
ক) Tk. 9423
খ
খ) Tk. 10250
গ
গ) Tk. 10500
ঘ
ঘ) Tk. 14000

ব্যাখ্যা

Sima : Rajon = (50000 × 36) : (80000 × 30)
1800000 : 2400000
= 3 : 4
∴ Sima's share = Tk. (24500 × 3/7)
= Tk. 10500.

১৫৩.

A bicycle marked at Tk. 2000 is sold for Tk. 1200 after two successive discounts. The first discount was 20%. Find the second discount percentage.

ক
35.75%
খ
25%
গ
30%
ঘ
20.25%

ব্যাখ্যা

Question: A bicycle marked at Tk. 2000 is sold for Tk. 1200 after two successive discounts. The first discount was 20%. Find the second discount percentage.

Solution:
Given that,
Original marked price = Tk. 2000
Final selling price after two successive discounts = Tk. 1200
First discount = 20%

Now,
Price after first discount = 2000 - 20% of 2000
= 2000 - (20/100) × 2000
= 2000 - 400
= Tk. 1600

Let the second discount be x%.
This discount is applied on Tk. 1600, and after the second discount, the selling price becomes Tk. 1200.
Discount amount in second discount = 1600 - 1200 = Tk. 400

So the second discount percentage ia,
⇒ x% of 1600 = 400
⇒ x = (400/1600) × 100
⇒ x = (1/4) × 100
∴ x = 25%

So the second discount is 25%.

১৫৪.

The price of a math book is Tk. 500, but you have only Tk. 350 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?

ক
Tk. 150
খ
Tk. 125
গ
Tk. 100
ঘ
Tk. 50

ব্যাখ্যা

Question: The price of a math book is Tk. 500, but you have only Tk. 350 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?

Solution:
In 20% discount,
Original price 100 taka then discount price 80 taka
Original price 1 taka then discount price 80/100 taka
Original price 500 Taka then discount price (80 × 500)/100 Taka
= 400 taka

I need to borrow = (400 - 350) Taka
= 50 taka

১৫৫.

A man buys tk. 50 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?

ক
ক) 35.50
খ
খ) 40
গ
গ) 48
ঘ
ঘ) 52

ব্যাখ্যা

Dividend on 1 share
= ( 10/ 100 ×50)
= Tk. 5
Tk. 12.50 is an income on an investment of tk. 100
Tk. 5 is an income on an investment of :
= Tk. (100× 2/25 ×5)
= Tk. 40.
∴ Cost of 1 share = Tk. 40

১৫৬.

As a salesperson, Rahim can choose one of two methods of annual payment: either an annual salary of Tk. 50,000 with no commission or an annual salary of Tk. 20,000 plus a 25 percent commission on his total annual sales. What must his total annual sales be to give him the same annual pay with either method?

ক
Tk. 1,00,000
খ
Tk. 1,20,000
গ
Tk. 1,50,000
ঘ
Tk. 80,000

ব্যাখ্যা

Question: As a salesperson, Rahim can choose one of two methods of annual payment: either an annual salary of Tk. 50,000 with no commission or an annual salary of Tk. 20,000 plus a 25 percent commission on his total annual sales. What must his total annual sales be to give him the same annual pay with either method?

Solution:
ধরি,
রহিমের মোট বার্ষিক বিক্রয় = x টাকা

প্রথম পদ্ধতি অনুযায়ী রহিমের বেতন = 50,000 টাকা
দ্বিতীয় পদ্ধতি অনুযায়ী রহিমের বেতন = 20,000 + x এর 25%

প্রশ্নমতে,
50000 = 20000 + (x এর 25%)
⇒ 50000 - 20000 = 25x/100
⇒ 30000 = x/4
⇒ x = 30000 × 4
∴ x = 120000

সুতরাং, রহিমের মোট বার্ষিক বিক্রয় 1,20,000 টাকা হতে হবে।

১৫৭.

To produce an annual income of Tk. 900 from a 9% stock at 90, the amount of stock needed is -

ক
ক) Tk. 10500
খ
খ) Tk. 10000
গ
গ) Tk. 10060
ঘ
ঘ) Tk. 18000

ব্যাখ্যা

Since face value is not given, take it as Tk. 100.
As it is an 9% stock, income (dividend) per stock = Tk. 9
ie, For an income of Tk. 9, the amount of stock needed = Tk. 100
For an income of Tk. 900, the amount of stock needed = (100 × 900)/9 = 10000

১৫৮.

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 B's share in it.

ক
4000
খ
5000
গ
6000
ঘ
7000

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 B's share in it.

Solution:
Suppose C's capital = x
then, B's capital = 4x (Since B's Capital is four times C's capital)
A's capital,
2 × A's capital = 3 × B's capital (Since twice A's capital is equal to thrice B's capital)
⇒ 2 × A = 3 × 4x
∴ A = 6x

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

B's share = 16500 × (4/11)
= 1500 × 4
= 6000

১৫৯.

X, Y & Z has started a business with a profit sharing ratio 7 : 8 : 9. If at the end of the year, Y gets a total of Taka 4,800 what will be X's profit?

ক
ক) Tk. 4,200
খ
খ) Tk. 4,000
গ
গ) Tk. 3,800
ঘ
ঘ) Tk. 3,600

ব্যাখ্যা

Question: X, Y & Z has started a business with a profit sharing ratio 7 : 8 : 9. If at the end of the year, Y gets a total of Taka 4,800 what will be X's profit?

Solution:
X, Y এবং Z এর লাভের অনুপাত = 7 : 8 : 9
X এর লাভের পরিমাণ = 7a
Y এর লাভের পরিমাণ = 8a
Z এর লাভের পরিমাণ = 9a

প্রশ্নমতে,
8a = 4800
a = 4800/8
a = 600

X এর লাভের পরিমাণ = 7 × 600 = 4200

১৬০.

The capital stock of a company is Tk. 500,000 and is divided into 5,000 shares. If the company declares a total dividend of Tk. 75,000, how much will Rahim receive for his 80 shares?

ক
Tk. 800
খ
Tk. 1,000
গ
Tk. 1,200
ঘ
Tk. 1,500

ব্যাখ্যা

Question: The capital stock of a company is Tk. 500,000 and is divided into 5,000 shares. If the company declares a total dividend of Tk. 75,000, how much will Rahim receive for his 80 shares?

Solution:
5,000 shares income Tk. 75,000
∴ 1 share income = Tk. 75,000 / 5,000
∴ 80 shares income = Tk. (75,000 × 80)/5,000
= Tk. 1,200

∴ Rahim will receive Tk. 1,200 as his share of the dividend.

১৬১.

If on a Sale there is 40% discount on the marked price of Tk. 1000, but the sale is done at Tk. 510 only then what additional discount % did the customer get?

ক
ক) 10%
খ
খ) 15%
গ
গ) 28%
ঘ
ঘ) 9%

ব্যাখ্যা

Question: If on a Sale there is 40% discount on the marked price of Tk. 1000, but the sale is done at Tk. 510 only then what additional discount % did the customer get?

Solution:

Marked price = Tk. 1000
First discount = 40%
After first discount selling price is = 1000 - (40% of 100) = 600

Let the second discount is = x%

ATQ,
600 - (x% of 600) =510
⇒ 600 - 6x = 510
⇒ 6x = 90
⇒ x = 15

১৬২.

If the list price of a book is Tk. 50, and a Tk. 10 discount is offered on the book, then what is the discount percentage?

ক
5%
খ
10%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: If the list price of a book is Tk. 50, and a Tk. 10 discount is offered on the book, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100

Marked Price = Tk. 50
Discount= Tk. 10

Discount (%) = (10/50) ×100%

= 100/5 %

= 20%

∴ Therefore, the discount percentage is calculated as 20%.

১৬৩.

What is the original price of a jacket if the sale price after 20% discount is Tk. 480?

ক
576
খ
600
গ
640
ঘ
660

ব্যাখ্যা

Question: What is the original price of a jacket if the sale price after 20% discount is Tk. 480?

Solution:
Let the original price be x

Discount = 20% of x
= 0.2x

Selling Price = Original Price - Discount
= x - 0.2x
= 0.8x

Now,
0.8x = 480
⇒ x = 480/0.8
∴ x = 600

∴ The original price of the jacket is Tk. 600

১৬৪.

X, Y and Z share Tk. 1,800 in such a way that X has 2.5 times as much as Y, and Y has 4 times as much as Z. How much money (in taka) does Z receive ?

ক
120
খ
132
গ
145
ঘ
200

ব্যাখ্যা

Question: X, Y and Z share Tk. 1,800 in such a way that X has 2.5 times as much as Y, and Y has 4 times as much as Z. How much money (in taka) does Z receive ?

Solution:
দেয়া আছে
x = 2.5y
y = 4z

x = 2.5 × 4z = 10z

x, y, z এর অনুপাত = 10z : 4z : z
= 10 : 4 : 1

z পাবে = 1800 এর 1/15 = 120 টাকা

১৬৫.

A discount of 15% on one article is the same as discount of 20% on a second article. The costs of the two articles can be-

ক
Tk. 85, Tk. 60
খ
Tk. 60, Tk. 40
গ
Tk. 40, Tk. 20
ঘ
Tk. 80, Tk. 60

ব্যাখ্যা

Question: A discount of 15% on one article is the same as discount of 20% on a second article. The costs of the two articles can be-

Solution:
Let the prices of two articles be X and Y
From the question 15X/100 = 20Y/100
⇒ 15X = 20Y
⇒ X/Y = 20/15

Thus the ratio of prices of two articles is = 20 : 15 = 4 : 3
Any two amounts in the ratio 4 : 3 will satisfy the condition.
In the above instance, Tk. 80 and Tk. 60 is the answer.

১৬৬.

Raju, Bappa and Samir divide Tk. 1,500 among them in such a way that if Tk. 50, Tk. 40 and Tk. 60 are removed from the sums that Raju, Bappa and Samir received respectively, then the shares will be in the ratio of 2 : 3 : 4. How much did Raju receive?

ক
Tk. 300
খ
Tk. 490
গ
Tk. 660
ঘ
Tk. 350

ব্যাখ্যা

Question: Raju, Bappa and Samir divide Tk. 1,500 among them in such a way that if Tk. 50, Tk. 40 and Tk. 60 are removed from the sums that Raju, Bappa and Samir received respectively, then the shares will be in the ratio of 2 : 3 : 4. How much did Raju receive?

সমাধান:
ধরি,
টাকা সরিয়ে নেওয়ার পর রাজু, বাপ্পা এবং সমীরের প্রাপ্ত অংশের অনুপাত যথাক্রমে 2x, 3x এবং 4x।

তাহলে, টাকা সরিয়ে নেওয়ার আগে তাদের প্রাপ্ত অংশ ছিল:
রাজু = 2x + 50
বাপ্পা = 3x + 40
সামীর = 4x + 60

তাদের প্রাপ্ত মোট টাকা হলো Tk. 1,500।
প্রশ্নমতে,
⇒ (2x + 50) + (3x + 40) + (4x + 60) = 1500
⇒ (2x + 3x + 4x) + (50 + 40 + 60) = 1500
⇒ 9x + 150 = 1500
⇒ 9x = 1500 - 150
⇒ 9x = 1350
⇒ x = 1350/9
∴ x = 150

রাজুর প্রাপ্ত টাকা = 2x + 50
= 2(150) + 50
= 300 + 50
= 350
সুতরাং, রাজু Tk. 350 পেয়েছিল।

১৬৭.

A, B and C enter into a partnership with the capital in the ratio 7/2 : 4/3 : 6/5. After 4 months A increases his share of capital by 50%. If at the end of the year the total profit earned is Tk. 2430, find the share of each in the profit.

ক
ক) 1680, 580, 450
খ
খ) 1575, 450, 405,
গ
গ) 1460, 415, 380
ঘ
ঘ) 1245, 380, 240

ব্যাখ্যা

Ratio of capitals = 7/2 : 4/3 : 6/5 = (7/2 × 30) : (4/3 × 30) : (6/5 × 30)
= 105 : 40 : 36.
Let the initial capitals of A, B and C be Tk. 105x, 40x, 36x respectively.
Then, ratio of profit = [105x × 4 + (150% of 105x) × 8] : (40x × 12 ) : (36x × 12)
1680 : 480 : 432
= 35 : 10 : 9.
∴ A's share = Tk. (2430 × 35/54) = Tk. 1575; B's share = Tk (2430 × 10/54) = Tk. 450
C's share = Tk. (2430 × 9/54) = Tk. 405.

১৬৮.

Three friends P, Q, and R share the cost of renting a storage unit. P stores goods weighing 300 kg for 4 months, Q stores 200 kg for 6 months, and R stores 400 kg for 3 months. If the total rent is Tk 840, how much should R pay as their share of rent?

ক
Tk. 280
খ
Tk. 190
গ
Tk. 300
ঘ
Tk. 220

ব্যাখ্যা

Question: Three friends P, Q, and R share the cost of renting a storage unit. P stores goods weighing 300 kg for 4 months, Q stores 200 kg for 6 months, and R stores 400 kg for 3 months. If the total rent is Tk 840, how much should R pay as their share of rent?

Solution:
Here,
P : Q : R = (300 × 4) : (200 × 6) : (400 × 3)
= 1200 : 1200 : 1200
= 1 : 1 : 1

∴ R's rent = {840 × (1/3)}
= Tk 280

১৬৯.

P and Q start a hotel. P left after 6 months. After the years ends P gets Tk. 6,000 as profit out of total profit of Tk. 9,000. What will be amount invested by Q if P had invested Tk. 20,000?

ক
ক) Tk. 6,000
খ
খ) Tk. 5,000
গ
গ) Tk. 4,500
ঘ
ঘ) Tk. 5,500

ব্যাখ্যা

মোট মুনাফা =৯০০০ টাকা
P মুনাফা পেল = ৬০০০ টাকা
Q মুনাফা পাবে = (৯০০০ - ৬০০০) টাকা
= ৩০০০ টাকা

P এবং Q এর মুনাফার অনুপাত = ৬০০০ : ৩০০০ = ২ : ১

Q বিনিয়োগ করেছিল x টাকা
প্রশ্নমতে,
২০০০০ × ৬ : x × ১২ = ২ :১
২০০০০ : ২x = ২ : ১
২০০০০/২x = ২/১
৪x = ২০০০০
x = ২০০০০/৪
x = ৫০০০

১৭০.

A fan is listed at Tk. 150 and a discount of 20% is given. Then the selling price is = ?

ক
ক) 180
খ
খ) 150
গ
গ) 120
ঘ
ঘ) 110

ব্যাখ্যা

Selling price = 150×80 / 100 = Tk. 120

১৭১.

Polash and Hasan started a business with the investment of Tk.6000 and Tk.5000 respectively and after 6 months, Mehedi joined with the investment of Tk.3000. At the end of the year, the total profit is Tk.5000. Find the Hasan’s profit share?

ক
Tk. 600
খ
Tk. 1200
গ
Tk. 2000
ঘ
Tk. 2400

ব্যাখ্যা

Question: Polash and Hasan started a business with the investment of Tk.6000 and Tk.5000 respectively and after 6 months, Mehedi joined with the investment of Tk.3000. At the end of the year, the total profit is Tk.5000. Find the Hasan’s profit share?

Solution:
Polash invest = 6000 × 12 =72,000
Hasan invest = 5000 × 12 = 60,000
Mehedi invest = 3000 × 6=18,000

The ratio of their investments is = 72,000 : 60,000 : 18,000
= 12 : 10 : 3

The total profit is Tk. 5000

Now,
Hasan’s share of the profit is = (10/25) × 5000 = 2000

∴ Hasan’s share of the profit is Tk. 2000

১৭২.

A and B start a business. A invests Tk 1,00,000 and B invests Tk 50,000. A works, B is a sleeping partner. A gets 20% of the profit for management. If total profit is Tk 30,000, what is A’s total share?

ক
Tk 22,000
খ
Tk 24,000
গ
Tk 20,000
ঘ
Tk 18,000

ব্যাখ্যা

Question: A and B start a business. A invests Tk 1,00,000 and B invests Tk 50,000. A works, B is a sleeping partner. A gets 20% of the profit for management. If total profit is Tk 30,000, what is A’s total share?

Solution:
First, A gets 20% of profit = 0.20 × 30,000 = Tk 6,000
Remaining = 24,000

→ This will be divided in the ratio of their investments: A : B = 100000 : 50000
→ divided in 2 : 1 ratio

A’s share from this = (2/3) × 24,000 = 16,000
Total A = 6,000 + 16,000 = Tk 22,000

১৭৩.

A, B and C start a business. A invests 3 times as much as B invests 2/3rd as much as C invests. Find the ratio of capitals of A, B and C ?

ক
ক) 6 : 2 : 3
খ
খ) 5 : 2 : 10
গ
গ) 6 : 10 : 3
ঘ
ঘ) 12 : 3 : 2

ব্যাখ্যা

Question: A, B and C start a business. A invests 3 times as much as B invests 2/3rd as much as C invests. Find the ratio of capitals of A, B and C ?

Solution:
ধরি
C বিনিয়োগ করে = x টাকা
B বিনিয়োগ করে = 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

১৭৪.

Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

ক
Tk. 29
খ
Tk. 35
গ
Tk. 30
ঘ
Tk. 25
ঙ
None

ব্যাখ্যা

Question: Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

Solution:
40% discount on 1000 = 1000 × 40% = 400

Two consecutive discounts on 1000.
30% discount on 1000 = 30% of 1000
= 300

After 30% discount on 1000 = 1000 - 300
= 700

Again,
After 10% discount on 700 = 10% of 700
= 70

Total discount = 300 + 70
= Tk. 370
So, the difference = 400 - 370
= Tk. 30

১৭৫.

P, Q, and R started a business by investing Tk. 120,000, Tk. 180,000 and Tk. 200,000 respectively. Find the share of Q out of an annual profit of Tk. 125,000.

ক
Tk. 45,000
খ
Tk. 50,000
গ
Tk. 55,000
ঘ
Tk. 35,000

ব্যাখ্যা

Question: P, Q, and R started a business by investing Tk. 120,000, Tk. 180,000 and Tk. 200,000 respectively. Find the share of Q out of an annual profit of Tk. 125,000.

Solution:
The ratio of investments of P, Q, and R is:
P : Q : R = 120,000 : 180,000 : 200,000
= 12 : 18 : 20
= 6 : 9 : 10

Sum of the ratios = 6 + 9 + 10 = 25
Total annual profit = Tk. 125,000

Q's share of profit = (9/25) × 125,000
= 9 × 5,000
= 45,000 Tk.

১৭৬.

The marked price of a t-shirt was Tk. 800. A man bought the same for Tk. 420 after getting two successive discounts. the first being 25%. then the second discount rate is-

ক
25%
খ
20%
গ
30%
ঘ
40%
ঙ
None

ব্যাখ্যা

Question: The marked price of a t-shirt was Tk. 800. A man bought the same for Tk. 420 after getting two successive discounts. the first being 25%. then the second discount rate is-

Solution:
Marked price = 800
Actual price = 420
First discount = 25%
Let the second discount be x%

Then, we can write

after 25% discount,
discounted amount = 800 × (25/100)
= 200

New price = 800 - 200
= 600 Tk

Again, second discount,
discounted amount = 600 × (x/100)
= 6x

New price = 600 - 6x

ATQ,
600 - 6x = 420
⇒ 600 - 420 = 6x
⇒ 6x = 180
⇒ x = 30

∴ Second discount = 30%

১৭৭.

After a 20% discount, the price of a television is Tk. 12000. What was the price before the discount?

ক
Tk. 18000
খ
Tk. 13000
গ
Tk. 14000
ঘ
Tk. 15000
ঙ
None of the above

ব্যাখ্যা

Question: After a 20% discount, the price of a television is Tk. 12000. What was the price before the discount?

Solution:
In 20% discount,
Discount price 80 taka when original price 100 taka

∴ Discount price 1 taka when original price 100/80 taka
∴ Discount price 12000 taka when original price
(12000 × 100)/80 taka
= 15000 taka

১৭৮.

X, Y, and Z invested Tk. 90000, Tk. 70000, Tk. 45000 respectively to start a business. At the end of 1 year, they earned a profit of Tk. 164000. What will be the Z’s share?

ক
ক) Tk. 3600
খ
খ) Tk. 5600
গ
গ) Tk. 7200
ঘ
ঘ) None of those.

ব্যাখ্যা

Question: X, Y, and Z invested Tk. 90000, Tk. 70000, Tk. 45000 respectively to start a business. At the end of 1 year, they earned a profit of Tk. 164000. What will be the Z’s share?

Solution:
Investment ration of X, Y & Z = 90000 : 70000 : 45000
= 18 : 14 : 9

Sum of the ration = (18 + 14 + 9)
= 41

∴ Z’s share = 164000 x (9/41)
= 36000

১৭৯.

A man purchased a shirt at Taka 300 after availing a discount of 25%. What is the catalog price of the shirt?

ক
ক) Tk 400
খ
খ) Tk 225
গ
গ) Tk 375
ঘ
ঘ) Tk 500

ব্যাখ্যা

25% discount এ
তালিকা মূল্য 100 টাকা হলে ক্রয়মূল্য = 100 - 25 = 75 টাকা

75 টাকা ক্রয়মূল্য হলে তালিকামূল্য = 100 টাকা
1 টাকা ক্রয়মূল্য হলে তালিকামূল্য = 100/75 টাকা
300 টাকা ক্রয়মূল্য হলে তালিকামূল্য = (100 × 300)/75 টাকা
= 400 টাকা

১৮০.

A, B, and C invest in a business in the ratio 2 : 1 : 3. If the total profit is Tk 30,000, how much more did C get than A?

ক
1000 Tk
খ
2000 Tk
গ
6000 Tk
ঘ
5000 Tk

ব্যাখ্যা

Question: A, B, and C invest in a business in the ratio 2 : 1 : 3. If the total profit is Tk 30,000, how much more did C get than A?

Solution:
Let the invested shares ratio = 2x : x : 3x

Now
2x + x + 3x = 30000
Or, 6x = 30,000
∴ x = 5,000

∴ A’s share = 2 × 5,000 = 10,000
∴ C’s share = 3 × 5,000 = 15,000
∴ Difference = 15,000 - 10,000
= Tk 5,000

∴ C gets 5000 Tk more than A.

১৮১.

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?

ক
Tk. 7500
খ
Tk. 8000
গ
Tk. 8500
ঘ
Tk. 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 × 12)/7x = 2/3
⇒ 14x = 126000
∴ x = 9000.

১৮২.

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 Taka 855, the total profit is?

ক
Tk. 2250
খ
Tk. 1500
গ
Tk. 2500
ঘ
Tk. 1800

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 Taka 855, the total profit is?

Solution:
Given that,
A and B invest in a business in the ratio = 3 : 2
5% of the total profit goes to charity
A’s share of the remaining profit = Tk. 855
Now,
Let the total profit = Tk. x
5% of x goes to charity, so the remaining profit = 95% of x = 95x/100
A’s share = (3/5)(95x/100) = 57x/100

ATQ,
⇒ 57x/100 = 855
⇒ x = (855 × 100)/57
⇒ x = 15 × 100
∴ x = 1500

∴ Total profit = Tk. 1500

১৮৩.

Ricky purchased a shirt for Tk. 2000. The discount offered for the shirt is 10%. Find how many takas has he given to the cashier?

ক
Tk. 1900
খ
Tk. 2200
গ
Tk. 1600
ঘ
Tk. 1800

ব্যাখ্যা

Question: Ricky purchased a shirt for Tk. 2000. The discount offered for the shirt is 10%. Find how many takas has he given to the cashier?

Solution:
Here,
Principal amount, p = Tk. 2000
Discount rate, r = 10%

Total Discount = p × r
= 2000 × 10% = 200

Dress price after discount = Principal amount - Total Discount
= 2000 - 200 = 1800

Ricky has given Tk. 1800 to the cashier.

১৮৪.

A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of -

ক
ক) Tk. 117.08
খ
খ) Tk. 109.70
গ
গ) Tk. 115.20
ঘ
ঘ) Tk. 105.09

ব্যাখ্যা

For an income of Tk. 10, investment = Tk. 96
For an income of 12, investment
= Tk. (96/10) × 12
= Tk. 115.20

Hence, He must purchase a stock worth of Tk. 115.20

১৮৫.

Asif, Sami and Riad started a shop by investing Tk. 2700, Tk. 9000 and Tk. 6300 respectively. At the end of one year, the profit was distributed. If Riad's share was Tk. 2100, what was their total profit?

ক
Tk. 5000
খ
Tk. 4000
গ
Tk. 7000
ঘ
Tk. 6000

ব্যাখ্যা

Question: Asif, Sami and Riad started a shop by investing Tk. 2700, Tk. 9000 and Tk. 6300 respectively. At the end of one year, the profit was distributed. If Riad's share was Tk. 2100, what was their total profit?

Solution:
Let the total profit is = x

Here, Asif : Sami : Riad = 2700 : 9000 : 6300
= 3 : 10 : 7

then, Riad's share = (7/20) × x = 7x/20
ATQ,
7x/20 = 2100
⇒ x = (2100 × 20)/7
∴ x = 6000

∴ The total profit = Tk. 6000

১৮৬.

A man invested Tk. 4455 in Tk. 10 shares quoted at Tk. 8.25. If the rate of dividend be 12%, his annual income is:

ক
ক) 207.40
খ
খ) 534.60
গ
গ) 648
ঘ
ঘ) 655.60

ব্যাখ্যা

Number of shares =4455/8.25= 540.
Face value = tk. (540 x 10) = tk. 5400.
Annual income = tk.12/100x 5400= tk. 648.

১৮৭.

Nila started a boutique shop by investing Tk. 25,000. After 4 months, Tania joined her with an investment of Tk. 35,000. After 2 year, the business earned a profit of Tk. 16,770. What was Nila's share in the profit?

ক
Tk. 7740
খ
Tk. 6850
গ
Tk. 6180
ঘ
Tk. 5900

ব্যাখ্যা

Question: Nila started a boutique shop by investing Tk. 25,000. After 4 months, Tania joined her with an investment of Tk. 35,000. After 2 year, the business earned a profit of Tk. 16,770. What was Nila's share in the profit?

Solution:
Ratio of capitals of Nila and Tania = (25000 × 24) : (35000 × 20)
= 600000 : 700000
= 6 : 7

Nila's share is = Tk. (16770 × 6)/13 = Tk. 7740.

১৮৮.

After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?

ক
Tk. 4800
খ
Tk. 5000
গ
Tk. 5500
ঘ
Tk. 4000

ব্যাখ্যা

Question: After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?

Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.

Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000

15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600

discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000

১৮৯.

The difference between discount of 35% and two successive discount of 20% on a certain bill was 22, the amount of the bill is = ?

ক
1500
খ
1800
গ
2200
ঘ
2400

ব্যাখ্যা

Question: The difference between discount of 35% and two successive discount of 20% on a certain bill was 22, the amount of the bill is = ?

Solution:
st discount = 35%
Single equivalent discount of 20% each
= [20 + 20 - {(20 × 20)/100}]%
= 36%

Difference = 36% - 35%
= 1%

Let the amount of the bill Tk. x
∴ (1/100) × x = 22
⇒ x/100 = 22
∴ x = 2200

১৯০.

A, B, and C invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If C's share of profit is Tk. 54000, find the total profit earned.

ক
135030
খ
130500
গ
145000
ঘ
None of these

ব্যাখ্যা

Question: A, B, and C invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If C's share of profit is Tk. 54000, find the total profit earned.

Solution:
Let the total profit = x
The ratio of investment = 63000 : 56000 : 84000
= 63 : 56 : 84
= 9 : 8 : 12
Now, sum of the ratios = 29

C's share = (12/29) × x = 54000
⇒ x = (54000 × 29)/12
x = 130500

Hence, the total profit = 130500

১৯১.

A and B started a business by investing Tk. 40,000 and Tk. 60,000 respectively. After 6 months, C joined the business by investing Tk. 80,000. What is the ratio of their profits at the end of the year?

ক
2 : 3 : 2
খ
4 : 3 : 5
গ
3 : 2 : 3
ঘ
1 : 2 : 3

ব্যাখ্যা

Question: A and B started a business by investing Tk. 40,000 and Tk. 60,000 respectively. After 6 months, C joined the business by investing Tk. 80,000. What is the ratio of their profits at the end of the year?

Solution:
Given,
A invests Tk. 40,000 for 12 months
∴ A’s investment = 40,000 × 12 = 4,80,000

B invests Tk. 60,000 for 12 months
∴ B’s investment = 60,000 × 12 = 7,20,000

C joins after 6 months and invests Tk. 80,000 for 6 months
∴ C’s investment = 80,000 × 6 = 4,80,000

Profit-sharing ratio A : B : C = 4,80,000 : 7,20,000 : 4,80,000
= 2 : 3 : 2 [divide all by 240000 to simplify]

১৯২.

Two friends A and B started a business with an initial capital contribution of Tk. 1 lac and Tk. 2 lacs. At the end of the year, the business made a profit of Tk. 30,000. Find the share of A in the profit.

ক
Tk. 15000
খ
Tk. 20000
গ
Tk. 18000
ঘ
Tk. 10000
ঙ
Tk. 25000

ব্যাখ্যা

Question: Two friends A and B started a business with an initial capital contribution of Tk. 1 lac and Tk. 2 lacs. At the end of the year, the business made a profit of Tk. 30,000. Find the share of A in the profit.

Solution:
We know that if the time period of investment is the same, profit/loss is divided by the ratio of the value of the investment.
Ratio of value of investment of A and B = 100000 : 200000 = 1 : 2
Ratio of share in profit = 1 : 2

Share of A in profit = (1/3) × 30,000 = Tk. 10000

১৯৩.

A package tour operator allows a 25% discount on his advertised price and then makes a profit of 20%. What is the advertised price on which he gains Tk. 60?

ক
520
খ
500
গ
480
ঘ
460

ব্যাখ্যা

Question: A package tour operator allows a 25% discount on his advertised price and then makes a profit of 20%. What is the advertised price on which he gains Tk. 60?

Solution:
Let,
the advertised price = x

Profit = Selling price - Cost Price = 60.
Selling price = 1.2 (C.P.)
∴ 1.2 C.P - C.P. = 60
⇒ 0.2 C.P. = 60
⇒ C.P. = 300
and Selling price = 360.

75% of x = 360
⇒ (75/100)x = 360
⇒ x = (360 × 100)/75
∴ x = 480

১৯৪.

A shopkeeper marks the price of an article at TK. 240. What will be the selling price. if he allows two successive discounts of 5% each ?

ক
Tk. 206.60
খ
Tk. 216.60
গ
Tk. 226.60
ঘ
Tk. 236.60

ব্যাখ্যা

Question: A shopkeeper marks the price of an article at TK. 240. What will be the selling price. if he allows two successive discounts of 5% each ?

Solution:

At 5% discount for the first time = (240 × 95)/100 = Tk.228

At 5% discount for second time = (228 × 95)/100 = Tk. 216.60

১৯৫.

Arif, Kamal and Shajib invested Tk.8000, Tk.4000 and Tk.8000 respectively in a business. Arif left after six months. If after eight months, there was a gain of Tk.4005, then what will be the share of Kamal in this gain?

ক
ক) 890 Taka
খ
খ) 1335 Taka
গ
গ) 1602 Taka
ঘ
ঘ) None of these

ব্যাখ্যা

প্রশ্ন: Arif, Kamal and Shajib invested Tk.8000, Tk.4000 and Tk.8000 respectively in a business. Arif left after six months. If after eight months, there was a gain of Tk.4005, then what will be the share of Kamal in this gain?

সমাধান:
Arif : Kamal : Shajib = (8000 x 6) : (4000 x 8) : (8000 x 8)
= 48 : 32 : 64
= 3 : 2 : 4

∴ Kamal's share = {4005 x (2/9)}
= 890 Taka

১৯৬.

A refrigerator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?

ক
40%
খ
60%
গ
55%
ঘ
45%

ব্যাখ্যা

Question: A refrigerator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?

Solution:
Let
x = original price.

First discount:
x(1 - 0.20)
= 0.80x (sale price).

Second discount:
0.80x(1 - 0.25)
= 0.60x (final sale price)

Therefore, the final price is 60% of the original price.
∴ the total discount = 1 - 0.60 = 0.40
∴ % total discount = 40%

১৯৭.

A, B and C enter into a partnership with a certain capital in which A's contribution is Tk.10,000. If out of a total profit of Tk. 1000, A gets Tk. 500, B gets Tk. 300 then C's capital is -

ক
ক) Tk. 5,000
খ
খ) Tk. 2,000
গ
গ) Tk. 4,000
ঘ
ঘ) Tk. 6,000

ব্যাখ্যা

According to the problem,
Total profit is = 1000 TK,
A’s profit = 500 TK
B’s profit = 300 TK
∴ C’s profit is = (Total profit – (A + B)’ profit) = (1000 − 800) = 200

∴ Profit Ratio between A, B and C is
⇒ 500 : 300 : 200
⇒ 5 : 3 : 2
Let their capitals be 5x, 3x, and 2x respectively.

According to the problem,
A’s contribution is TK. 10000.
∴ 5x = 10000
⇒ x = 2000

∴ C’s share = 2x
= 2 × 2000
= 4000Tk

১৯৮.

A shopkeeper offers two successive discounts of 10% and 20% on an item marked at 1,000 Taka. What is the final selling price?

ক
680 Taka
খ
720 Taka
গ
750 Taka
ঘ
780 Taka

ব্যাখ্যা

Question: A shopkeeper offers two successive discounts of 10% and 20% on an item marked at 1,000 Taka. What is the final selling price?

Solution:
New Price after First Discount:
1000 - 10% of 1000
= 1000 - 100
= 900 Taka

∴ Final selling price = 900 - 20% of 900
= 900 - 180
= 720 Taka

১৯৯.

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. 6600. What is the share of B?

ক
1100
খ
1150
গ
1175
ঘ
1200

ব্যাখ্যা

Question: 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. 6600. What is the share of B?

Solution:
A invests 3 times as much as B invests and B invests two third of what C invests.
Let,
C invests = x
B invests = 2x/3
A invests = 3 × (2x/3) = 2x

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

The share of B = (2/11) × 6600
= 1200

২০০.

The banker's gain on a sum due 2 years hence at 10% per annum is 320 Tk. The banker's discount is:

ক
1600 Tk
খ
1920 Tk
গ
2100 Tk
ঘ
2550 Tk
ঙ
2820 Tk

ব্যাখ্যা

Question: The banker's gain on a sum due 2 years hence at 10% per annum is 320 Tk. The banker's discount is:

Solution:
Here,
Banker’s Gain (B.G) = 320 Tk
Rate (R) = 10%
Time (T) = 2 years

We know,
True Discount (T.D) = B.G/(R × T)
= (320 × 100)/(10 × 2)
= 3200/2
= 1600 Tk

∴ Banker’s Discount (B.D) = 1600 + 320
= 1920 Tk