Question

A, B and C enter into a partnership in the ratio \( \frac{7}{2} : \frac{4}{3} : \frac{5}{6} \). After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21,600 then B's share in the profit is:

• A. Rs. 2,100
• B. Rs. 2,400
• C. Rs. 3,600
• D. Rs. 4,000

Hint:

When a partner changes their investment part-way through the term, adjust their share proportionally for the time invested before and after the change.

Answer 1

The Correct Option is D

A, B, and C enter into a partnership with initial shares in the ratios \( \frac{7}{2} \), \( \frac{4}{3} \), and \( \frac{6}{5} \). To work with simpler numbers, these ratios are normalized to simpler integers proportional to their original values:

\[ A = 7 \times 15 = 105, \quad B = 4 \times 10 = 40, \quad C = 6 \times 6 = 36. \]

After 4 months, A increases his share by 50%. Therefore, his new share is:

\[ 157.5 = 105 + \frac{50\% \times 105}{100} = 105 + 52.5 \]

The investment durations are as follows:

• A invests 105 units for 4 months and 157.5 units for the next 8 months.
• B invests 40 units for 12 months.
• C invests 36 units for 12 months.

The total investment-time product is:

\[ \text{A}: 105 \times 4 + 157.5 \times 8 = 420 + 1260 = 1680, \quad \text{B}: 40 \times 12 = 480, \quad \text{C}: 36 \times 12 = 432. \]

The total investment-time ratio of A:B:C is \( 1680:480:432 \). Given that the total profit at the end of one year is Rs. 21,600, B's share of the profit is calculated as follows:

\[ \text{B's share} = \frac{480}{2592} \times 21600 = \frac{480 \times 21600}{2592} = \text{Rs.}\ 4000 \]

Thus, B's share of the profit is Rs. 4,000.