A. B and C are partners in a business. Their shares are in the proposition of

1/3:1/4:1/5.

A withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of C is-

Question:

A, B, and C are partners in a business. Their shares are in the proportion of 13:14:15. A withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of C is:

Choices:

1. Tk. 1240

2. Tk. 1250

3. Tk. 1300

4. Tk. 1400

The correct answer is Tk. 1240.

Reasoning:

To determine why Tk. 1240 is the correct answer, let's break down the problem. We need to consider the capital contributed by each partner and the duration for which it was active.

Step-by-Step Calculation:

1. Initially, let the shares of A, B, and C be denoted by the capital $A$, $B$, and $C$ respectively in the proportions 13:14:15.

2. Suppose the common multiplier is $x$, then their initial investments are:

   • $ \text{A's capital} = 13x $

   • $ \text{B's capital} = 14x $

   • $ \text{C's capital} = 15x $

3. A withdraws half of his capital after 15 months:

   • For the first 15 months, A's investment is $13x$

   • For the next 15 months, A's investment is $ \frac{13x}{2} $

4. B and C do not withdraw their investments:

   • B's investment for 30 months is $14x$

   • C's investment for 30 months is $15x$

5. Calculating the effective capital contribution (investment * time):

   • A's contribution: $13x \times 15 + \frac{13x}{2} \times 15 = 195x$

   • B's contribution: $14x \times 30 = 420x$

   • C's contribution: $15x \times 30 = 450x$

6. Total contribution:

   $ 195x + 420x + 450x = 1065x $

7. The profit of Tk. 4340 is distributed in proportion to their contributions:

   • Share of C:

     $ \text{C's share} = \frac{450x}{1065x} \times 4340 $

   • Simplify the ratio:

     $ \frac{450}{1065} = \frac{450 \div 15}{1065 \div 15} = \frac{30}{71} $

   • C's share in profit:

     $ \text{C's share} = \frac{30}{71} \times 4340 $

     $ \text{C's share} = 1830 \div 71 $

     $ \text{C's share} = 1240 $

Therefore, the share of C in the profit is Tk. 1240, which matches option (a).