Multiple choice

A group of three friends named Ria, Reena and Richa initiated a gift packing business by infusing Rs. 26,000, Rs. 39,000 and Rs. 52,000, respectively. Richa quit the partnership after 8 months. The business attained a profit of Rs. 46,000 after completion of one year. Calculate the amount that Richa holds in the profits.

  1. Rs. 16,000

  2. Rs. 18,000

  3. Rs. 24,000

  4. Rs. 20,444.4

  5. Rs. 26,000
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A Correct answer
Explanation

Investment ratio: 26:39:52 = 2:3:4. Time ratio: 12:12:8 = 3:3:2. Profit ratio = (2*3):(3*3):(4*2) = 6:9:8. Total parts = 23. Richa's share = (8/23) * 46,000 = 8 * 2,000 = 16,000.

AI explanation

To find the profit share, multiply each partner's investment by the number of months they invested, giving the ratio 26000 times 12 to 39000 times 12 to 52000 times 8. This simplifies to 312000 to 468000 to 416000, which further reduces to the ratio 39 to 58.5 to 52. Richa's share of the total profit is 52 parts out of 149.5, so her profit is 52/149.5 times 46000, which equals exactly Rs. 16000.

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