Question

A starts a business with ₹ 42,000 and is joined afterwards by B with ₹ 72,000. After how many months did B join if the profits at the end of the year are divided equally?

• A. 4
• B. 5
• C. 7
• D. 8

Hint:

The profits are divided in proportion to the product of investment and time. Use this concept to solve profit-sharing problems.

Answer 1

The Correct Option is B

The profits are divided based on the product of the amount invested and the time for which the investment was made. Let \( t \) be the number of months A worked. A’s investment is ₹ 42,000 for 12 months. So, A’s share of the profit is proportional to \( 42,000 \times 12 \). When B joins, the amount invested by B is ₹ 72,000. B’s share is proportional to \( 72,000 \times t \). For equal profit distribution, the proportion of investments for both must be equal: \[ 42,000 \times 12 = 72,000 \times t \] Solving for \( t \): \[ t = \frac{42,000 \times 12}{72,000} = 5 \text{ months}. \] Thus, B joined after 5 months.