A, B, C started a business with their investments in the ratio 1:3:5. After 4…

2025

A, B, C started a business with their investments in the ratio 1:3:5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is:

  1. A.

    1:2:3

  2. B.

    3:4:15

  3. C.

    3:5:10

  4. D.

    5:6:10

Show answer & explanation

Correct answer: D

Concept: When capital invested by partners changes at some point during the year, the profit-sharing ratio equals the ratio of each partner's total (Capital × Time), computed by adding up the capital-time products for every period during which that partner's capital remained constant — not simply the initial investment ratio.

Application:

  1. Let the initial investments of A, B and C be 1x, 3x and 5x respectively, matching the given ratio 1:3:5.

  2. After 4 months, A invests the same amount again, so A's capital becomes 1x + 1x = 2x for the remaining 8 months.

  3. B and C each withdraw half of their investment, so B's capital becomes 3x − 1.5x = 1.5x and C's capital becomes 5x − 2.5x = 2.5x for the remaining 8 months.

  4. A's capital × time = (1x × 4) + (2x × 8) = 4x + 16x = 20x.

  5. B's capital × time = (3x × 4) + (1.5x × 8) = 12x + 12x = 24x.

  6. C's capital × time = (5x × 4) + (2.5x × 8) = 20x + 20x = 40x.

  7. So the profit ratio A:B:C = 20x : 24x : 40x, which simplifies (dividing by 4x) to 5:6:10.

Cross-check: 20 + 24 + 40 = 84, and 5 + 6 + 10 = 21; 84 ÷ 21 = 4, confirming the simplification 20:24:40 = 5:6:10 is consistent.

Explore the full course: Capgemini Preparation