Multiple choice

Choose the correct answer from the alternatives given. Three partners invested capital in the ratio $2 : 7 : 9$. The time period for which each of them invested was in the ratio of the reciprocals of the amount invested. Find the share of the partner who brought in the highest capital, if profit is Rs. $1080$.

  1. Rs. $120$
  2. Rs. $360$
  3. Rs. $540$
  4. Rs. $420$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Capital ratio = 2:7:9. Time ratio = 1/2 : 1/7 : 1/9. Multiply by LCM (126) to get time ratio = 63 : 18 : 14. Profit ratio = Capital * Time = (2*63) : (7*18) : (9*14) = 126 : 126 : 126 = 1 : 1 : 1. Total profit = 1080. Each partner gets 1080 / 3 = 360.

AI explanation

The profit ratio is based on the product of capital and time, where the time periods are the reciprocals of the capital amounts. The capital ratio is 2 : 7 : 9, so the time ratio is 1/2 : 1/7 : 1/9, and multiplying them gives profit ratios of 1, 1, and 1 respectively. This means the total profit of Rs. 1080 is divided equally into three parts of 1080 / 3 = 360. The partner with the highest capital therefore receives Rs. 360.

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