A, B and C become partners in a business. A contributes1/3rd of the capital for1/4th of the time. B contributes1/5th of the capital for1616th of the time and C the rest of the capital for the whole time. If the profit is Rs. 1820, then the A's share in profit is ?a)Rs. 130b)Rs. 260c)Rs. 292d)Rs. 304Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given information:
- A contributes 1/3rd of the capital for 1/4th of the time.
- B contributes 1/5th of the capital for 16/16th of the time.
- C contributes the rest of the capital for the whole time.
- The profit is Rs. 1820.

Let's calculate the ratio of their contributions in terms of capital and time.

Calculating A's contribution:
- A contributes 1/3rd of the capital for 1/4th of the time.
- Let's assume the total capital is C and the total time is T.
- A's capital contribution = (1/3) x C
- A's time contribution = (1/4) x T

Calculating B's contribution:
- B contributes 1/5th of the capital for 16/16th of the time.
- B's capital contribution = (1/5) x C
- B's time contribution = (16/16) x T = T

Calculating C's contribution:
- C contributes the rest of the capital for the whole time.
- C's capital contribution = C
- C's time contribution = T

Now, let's calculate their profit shares based on their contributions.

Calculating A's share:
- A's share = (A's capital contribution x A's time contribution) / (Total capital x Total time) x Profit
- A's share = ((1/3) x C x (1/4) x T) / (C x T) x 1820
- A's share = (1/12) x 1820
- A's share = Rs. 151.67

Calculating B's share:
- B's share = (B's capital contribution x B's time contribution) / (Total capital x Total time) x Profit
- B's share = ((1/5) x C x T) / (C x T) x 1820
- B's share = (1/5) x 1820
- B's share = Rs. 364

Calculating C's share:
- C's share = (C's capital contribution x C's time contribution) / (Total capital x Total time) x Profit
- C's share = (C x T) / (C x T) x 1820
- C's share = 1820

Therefore, A's share in the profit is Rs. 151.67, B's share is Rs. 364, and C's share is Rs. 1820.

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