Question

A started a business with Rs.21,000 and is joined afterwards by B with Rs.36,000. After how many months did B join if the profit at the end of the year is divided equally?

• A. 3 months
• B. 4 months
• C. 5 months
• D. 6 months

Hint:

When solving for investment times in partnership problems, set up equations based on the total contributions (investment \(\times\) time) being proportional to the profit shares.

Answer 1

The Correct Option is C

Step 1: Set up the equation for the profit shares.
Let \( m \) be the number of months B joined after. A invests for 12 months, and B invests for \( 12 - m \) months.

Step 2: Calculate their investment ratios.
\[ \text{A's Investment} = 21000 \times 12, \quad \text{B's Investment} = 36000 \times (12 - m) \] Given that their profits are equal: \[ 21000 \times 12 = 36000 \times (12 - m) \] \[ 252000 = 36000 \times (12 - m) \] \[ \frac{252000}{36000} = 12 - m \] \[ 7 = 12 - m \] \[ m = 5 \]