A, B and C enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4…

2023

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

  1. A.

    Rs.6000

  2. B.

    Rs.5000

  3. C.

    Rs.3500

  4. D.

    Rs. 4000

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Correct answer: D

Key idea: convert the fractional ratios to whole numbers and use time-weighted contributions (capital × time).

  1. Convert the given ratios to whole numbers by multiplying by LCM of denominators (2, 3, 5) = 30: 7/2 × 30 = 105, 4/3 × 30 = 40, 6/5 × 30 = 36. So initial investments are proportional to 105 : 40 : 36.

  2. A increases his investment by 50% after 4 months. So A invests 105 for the first 4 months and 105 × 1.5 = 157.5 for the remaining 8 months. Time-weighted contribution of A = 105×4 + 157.5×8 = 420 + 1260 = 1680.

  3. Time-weighted contribution of B = 40 × 12 = 480 (B’s investment unchanged for the full year).

  4. Time-weighted contribution of C = 36 × 12 = 432 (C’s investment unchanged for the full year).

  5. So the profit-sharing ratio is 1680 : 480 : 432. Divide by 48 to simplify: 35 : 10 : 9. Total parts = 35 + 10 + 9 = 54.

  6. B’s fraction of the profit = 10/54 = 5/27. Therefore B’s share = 21600 × 10/54 = 21600 × 5/27 = Rs. 4000.

Answer: Rs. 4000

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