Profit and Loss Easy Questions and Answers | Page - 116

Profit and Loss

A, B and C entered into a business and the ratio of their investments was 5 : 4 : 3. After 4 months B invested $ 1,000 more and after 8 months C invested $ 2,000 more. At the end of one year the profit ratio was 15 : 14 : 11, then the investment of C at the beginning was

1. $ 3000
1. $ 6000
1. $ 4500
1. $ 7500

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Here , Ratio of profit of A , B and C = 15 : 14 : 11
Ratio of their investments = 5 : 4 : 3
Let the investment of A = $ 5k
The investment of B = $ 4k
The investment of C = $ 3k
∴ Ratio of their equivalent capitals for 1 month = { 5k × 12 } : { 4k × 4 + ( 4k + 1000 ) × 8 } : { 3k × 8 + ( 3k + 2000 ) × 4 }
Ratio of their equivalent capitals for 1 month = 15k : (12k + 2000) : (9k + 2000)
∴ 15k =
15
12k + 2000 14

Correct Option: A

Here , Ratio of profit of A , B and C = 15 : 14 : 11
Ratio of their investments = 5 : 4 : 3
Let the investment of A = $ 5k
The investment of B = $ 4k
The investment of C = $ 3k
∴ Ratio of their equivalent capitals for 1 month = { 5k × 12 } : { 4k × 4 + ( 4k + 1000 ) × 8 } : { 3k × 8 + ( 3k + 2000 ) × 4 }
Ratio of their equivalent capitals for 1 month = 15k : (12k + 2000) : (9k + 2000)
∴ 15k =
15
12k + 2000 14

⇒ 14k = 12k + 2000
⇒ 2k = 2000
⇒ k = $ 1000
∴ C’s investment = 3k = $ 3000

A began business with $ 45000 and was joined afterwards by B with $ 54000. After how many months did B join if the profits at the end of the year were divided in the ratio 2 : 1?

1. 4
1. 5
1. 6
1. 7

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Let B remained in business for T months.
Invested amount by A = $ 45000
Invested amount by B = $ 54000
Ratio of profit of A and B = 2 : 3
Ratio of equivalent capitals = 45000 × 12 : 54000 × T = 10 : T
∴ 10 =
2
T 1

Correct Option: D

Let B remained in business for T months.
Invested amount by A = $ 45000
Invested amount by B = $ 54000
Ratio of profit of A and B = 2 : 3
Ratio of equivalent capitals = 45000 × 12 : 54000 × T = 10 : T
∴ 10 =
2
T 1

⇒ 2T = 10 ⇒ T = 5
Clearly, B joined after (12 – 5) = 7 months.

A starts business with $ 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?

1. $ 8000/-
1. $ 8500/-
1. $ 9000/-
1. $ 7500/-

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As per the given question ,
A’s investment of $ 3500 is for 12 months
Let B’s investment be p for 7 months only.
At the end of the year the profit is divided in the ratio 2 : 3 and it must be equal to the ratio of the product, (Amount × time)
Here , T₁ = 12 months , A₁ = $ 3500 , T₂ = 7 months , A₂ = $ p
T₁ × A₁ = Ratio of Profit
T₂ × A₂

⇒ 12 × 3500 = 2
7p 3

Correct Option: C

As per the given question ,
A’s investment of $ 3500 is for 12 months
Let B’s investment be p for 7 months only.
At the end of the year the profit is divided in the ratio 2 : 3 and it must be equal to the ratio of the product, (Amount × time)
Here , T₁ = 12 months , A₁ = $ 3500 , T₂ = 7 months , A₂ = $ p
T₁ × A₁ = Ratio of Profit
T₂ × A₂

⇒ 12 × 3500 = 2
7p 3

⇒ p = 12 × 3500 × 3
7 2

or p = 9000
∴ B’s investment is $ 9000.

In a business partnership among A, B, C and D, the profit is shared as follows:
A’s share = B’s share = C’s share = 1
B’s share C’s share D’s share 3

If the total profit is $ 4,00,000, then, the share of C is

1. $ 1,12,500
1. $ 1,37,500
1. $ 90,000
1. $ 2,70,000

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Given that , Total profit = $ 4,00,000
A : B = 1 : 3
B : C = 1 : 3 = 3 : 9
C : D = 1 : 3 = 9 : 27
∴ A : B : C : D = 1 : 3 : 9 : 27
Sum of ratios = 1 + 3 + 9 + 27 = 40
∴ C’s share in profit = ratio of C × Total profit
Sum of ratios

Correct Option: C

Given that , Total profit = $ 4,00,000
A : B = 1 : 3
B : C = 1 : 3 = 3 : 9
C : D = 1 : 3 = 9 : 27
∴ A : B : C : D = 1 : 3 : 9 : 27
Sum of ratios = 1 + 3 + 9 + 27 = 40
∴ C’s share in profit = ratio of C × Total profit
Sum of ratios

C’s share in profit = 9 × 400000 = $ 90,000
40

A, B and C started a business by investing $ 40500, $ 45000 and $ 60000 respectively. After 6 months C withdrew $ 15000 while A invested $ 4500 more. In annual profit of $ 56100, the share of C will exceed that of A by

1. $ 900
1. $ 1100
1. $ 3000
1. $ 3900

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Given in question , Total profit = $ 56100
∴ Ratio of equivalent capitals of A, B and C for 1 month = { 40500 × 6 + ( 40500 + 4500 ) × 6 } : { 45000 × 12 } : { 60000 × 6 + ( 60000 - 15000 ) × 6 }
Ratio of equivalent capitals of A, B and C for 1 month = (40500 × 6 + 45000 × 6) : (45000 × 12) : (60000 × 6 + 45000 × 6)
Ratio of equivalent capitals of A, B and C for 1 month = (405 + 450) : (450 × 2) : (600 + 450) = 855 : 900 : 1050
Ratio of equivalent capitals of A, B and C for 1 month = 171 : 180 : 210 = 57 : 60 : 70
Sum of the ratios = 57 + 60 + 70 = 187

Correct Option: D

Given in question , Total profit = $ 56100
∴ Ratio of equivalent capitals of A, B and C for 1 month = { 40500 × 6 + ( 40500 + 4500 ) × 6 } : { 45000 × 12 } : { 60000 × 6 + ( 60000 - 15000 ) × 6 }
Ratio of equivalent capitals of A, B and C for 1 month = (40500 × 6 + 45000 × 6) : (45000 × 12) : (60000 × 6 + 45000 × 6)
Ratio of equivalent capitals of A, B and C for 1 month = (405 + 450) : (450 × 2) : (600 + 450) = 855 : 900 : 1050
Ratio of equivalent capitals of A, B and C for 1 month = 171 : 180 : 210 = 57 : 60 : 70
Sum of the ratios = 57 + 60 + 70 = 187
Required difference = 70 - 57 × 56100
187

Required difference = 13 × 56100 = $ 3900
187