Multiple choice

P, Q & R enter into a partnership to construct a school by investing in the ratio of 5:4:6. After 1 year, Q invests another Rs. 240000. And after one year R also invests Rs. 240000. At the end of 3 yrs profits are shared in the ratio of 5:6:7. Find the initial investment of Q.

  1. Rs.320000

  2. Rs.240000

  3. Rs.160000

  4. Rs.480000

  5. None of these
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A Correct answer
Explanation

Let initial investments be 5x, 4x, 6x. Profit ratio = (Investment * Time). P: 5x*3 = 15x. Q: 4x*1 + (4x+240000)*2 = 12x + 480000. R: 6x*2 + (6x+240000)*1 = 18x + 240000. Given Q's share/P's share = 6/5: (12x+480000)/15x = 6/5 -> 60x + 2400000 = 90x -> 30x = 2400000 -> x = 80000. Q's initial investment = 4x = 320000.

AI explanation

Let the initial investments be 5x, 4x, and 6x. The profit ratio equals the ratio of effective capital, so for Q we have 4x times 3 plus 240000 times 2, which equals 12x plus 480000, and for R we have 6x times 3 plus 240000 times 1, which equals 18x plus 240000. Since the profit ratio of P to Q to R is 5 to 6 to 7, P's share of 15x corresponds to 5 parts, meaning one part equals 3x; setting Q's 12x plus 480000 equal to 6 times 3x gives an impossible negative, so instead setting Q's share equal to 6 parts yields 12x plus 480000 equals 18x, making x equal to 80000. Q's initial investment is 4x, which is Rs. 320000.

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