Question

A and B started a business with investment of Rs.90,000 and Rs.80,000 respectively. After 5 months, B left the business and C joined with a capital which is Rs.60,000 less than that of B. If at the end of the year, the share of C in the profit was Rs.42,000, then find the total profit earned at the end of the year.

• A. Rs.2,16,000
• B. Rs.2,36,000
• C. Rs.2,40,000
• D. Rs.4,86,000

Hint:

In partnership problems, the profit is shared in the ratio of the product of the investment and the time period for which it was invested. This product is sometimes called the "equivalent capital".

Answer 1

The Correct Option is D

Step 1: Calculate the investment period for each partner. The business runs for a year (12 months).

A's investment period = 12 months.
B left after 5 months, so B's investment period = 5 months.
C joined after 5 months, so C's investment period = 12 - 5 = 7 months.

Step 2: Calculate the capital for each partner.

A's capital = Rs.90,000.
B's capital = Rs.80,000.
C's capital = B's capital - Rs.60,000 = Rs.80,000 - Rs.60,000 = Rs.20,000.

Step 3: Find the ratio of their effective investments (Capital × Time).

A's share ratio = 90,000 × 12 = 1,080,000
B's share ratio = 80,000 × 5 = 400,000
C's share ratio = 20,000 × 7 = 140,000
The profit-sharing ratio is A : B : C = 1,080,000 : 400,000 : 140,000. Simplifying by dividing by 20,000, we get the ratio: 54 : 20 : 7.

Step 4: Calculate the total profit based on C's share. The total parts in the ratio are 54 + 20 + 7 = 81 parts. We are given that C's share of the profit (which is 7 parts) is Rs.42,000. So, 7 parts = Rs.42,000. 1 part = Rs.42,000 / 7 = Rs.6,000. The total profit is 81 parts. Total Profit = 81 × Rs.6,000 = Rs.4,86,000.
Note: The calculated total profit of Rs.4,86,000 does not match any of the given options. There might be an error in the question's data or the options provided.