Question

A, B and C start a business each investing Rs. 20,000. After 5 months A withdrew Rs.5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of A.

• A. Rs 20500
• B. Rs 21200
• C. Rs 28200
• D. Rs 27300

Answer 1

Answer: (A)

Rs. 20,500

Answer 2

The problem involves calculating the share of profit for each partner based on their varying investments over a year. The profit is distributed in the ratio of the product of capital and time for each partner.

1. Calculate A's equivalent capital for 1 year:

A invested Rs. 20,000 for the first 5 months.
After 5 months, A withdrew Rs. 5,000, so the capital for the remaining 7 months (12 - 5) was Rs. (20,000 - 5,000) = Rs. 15,000.
A's equivalent capital = $(20,000 \times 5) + (15,000 \times 7)$
$= 100,000 + 105,000$
$= \text{Rs. } 205,000$

2. Calculate B's equivalent capital for 1 year:

B invested Rs. 20,000 for the first 5 months.
After 5 months, B withdrew Rs. 4,000, so the capital for the remaining 7 months was Rs. (20,000 - 4,000) = Rs. 16,000.
B's equivalent capital = $(20,000 \times 5) + (16,000 \times 7)$
$= 100,000 + 112,000$
$= \text{Rs. } 212,000$

3. Calculate C's equivalent capital for 1 year:

C invested Rs. 20,000 for the first 5 months.
After 5 months, C invested Rs. 6,000 more, so the capital for the remaining 7 months was Rs. (20,000 + 6,000) = Rs. 26,000.
C's equivalent capital = $(20,000 \times 5) + (26,000 \times 7)$
$= 100,000 + 182,000$
$= \text{Rs. } 282,000$

4. Determine the ratio of their equivalent capitals (and thus their profit shares):

Ratio of A : B : C = $205,000 : 212,000 : 282,000$
Simplifying by dividing by 1,000:
Ratio of A : B : C = $205 : 212 : 282$

5. Calculate the total sum of the ratio parts:

Total ratio parts = $205 + 212 + 282 = 699$

6. Calculate A's share of the total profit:

Total profit = Rs. 69,900
A's share = $\left(\frac{\text{A's ratio part}}{\text{Total ratio parts}}\right) \times \text{Total profit}$
A's share = $\left(\frac{205}{699}\right) \times 69,900$
A's share = $205 \times \left(\frac{69,900}{699}\right)$
A's share = $205 \times 100$
A's share = $\text{Rs. } 20,500$

The share of A is Rs. 20,500.