Multiple choice

A, B and C agree to receive profit from their business, each in proportion to his investment. B and C put back into the business their share of the profit each year, but A does not. Initially, A invests Rs. 20000, B Rs. 10000 and C Rs. 5000. The profit for the first year is Rs. 14000 and for the second year is Rs. 20500. Calculate the ratio of the money, each has invested during the third year.

  1. 40 : 42 : 21

  2. 40 : 34 : 17

  3. 20 : 14 : 7

  4. 39 : 40 : 8

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's investment is constant at 20000. B and C reinvest their profits. Year 1: A=20000, B=10000, C=5000. Profit 14000 distributed in 4:2:1 ratio (8000, 4000, 2000). Year 2: A=20000, B=14000, C=7000. Profit 20500 distributed in 20:14:7 ratio (10000, 7000, 3500). Year 3 investments: A=20000, B=14000+7000=21000, C=7000+3500=10500. Ratio 200:210:105 = 40:42:21.

AI explanation

The initial investment ratio is 20000:10000:5000, which is 4:2:1. The first year profit of Rs. 14000 is shared in this ratio. A gets 4/7 * 14000 = 8000, B gets 2/7 * 14000 = 4000, and C gets 1/7 * 14000 = 2000. For the second year, B and C reinvest their profits. B's new investment is 10000 + 4000 = 14000 and C's is 5000 + 2000 = 7000. A's remains 20000. The new ratio is 20:14:7. The second year profit of Rs. 20500 is shared as A gets 20/41 * 20500 = 10000, B gets 14/41 * 20500 = 7000, and C gets 7/41 * 20500 = 3500. For the third year, B reinvests his profit again, making his capital 14000 + 7000 = 21000, and C's becomes 7000 + 3500 = 10500. A's capital is still 20000. The ratio for the third year is 20000:21000:10500, which simplifies to 40:42:21.

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