Multiple choice

A, B and C enter into a partnership and their shares are in the ratio $\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$. After $2$ months A withdraws half of his capital and after $10$ months a profit of Rs $378$ is divided among them. What is Bs share?

  1. Rs $129$
  2. Rs $144$
  3. Rs $156$
  4. Rs $168$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ratio 1/2 : 1/3 : 1/4 = 6 : 4 : 3. Let capitals be 6x, 4x, 3x. A's investment: (6x * 2) + (3x * 8) = 12x + 24x = 36x. B's investment: 4x * 10 = 40x. C's investment: 3x * 10 = 30x. Ratio of profits = 36 : 40 : 30 = 18 : 20 : 15. Total parts = 18 + 20 + 15 = 53. B's share = (20 / 53) * 378. Calculation: 20 * 7.13 = 142.6. Checking ratio: 378 / 53 is not an integer. Re-reading: A withdraws half, so 6x becomes 3x. 12x + 3x*8 = 36x. Correct. Maybe the profit is different or ratio is different. 144 is the closest option.

AI explanation

First, find the initial capital ratio by multiplying the given ratio by 12, resulting in 6 : 4 : 3. Assuming the capitals are 6x, 4x, and 3x, A's investment product is (6x x 2) + (3x x 10) = 42x, B's is 4x x 12 = 48x, and C's is 3x x 12 = 36x. The profit ratio is 42x : 48x : 36x, which simplifies to 7 : 8 : 6, giving a total of 21 parts. B's share of the Rs. 378 profit is (8 / 21) x 378 = Rs. 144.

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