Multiple choice

Veer and Manyu entered into a business by investing Rs. 6000 and Rs. 8000 for x and (x+4) months respectively. At the end, profit share of Veer is 3900 Rs. less than profit share of Manyu. Find the value of x if total profit is Rs. 12900. (in months)

  1. 12

  2. 8

  3. 6

  4. 10

  5. 4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ratio of investments: 6000x : 8000(x+4) = 3x : 4(x+4). Profit share difference: (4(x+4) - 3x) / (3x + 4x + 16) * 12900 = 3900. (x+16)/(7x+16) = 3900/12900 = 39/129 = 13/43. 43x + 688 = 91x + 208. 48x = 480. x = 10.

AI explanation

Let Manyu's profit be M and Veer's profit be V; then M - V = 3900 and M + V = 12900. Solving these equations gives Manyu's share as 8400 and Veer's share as 4500, making their profit ratio 4500 : 8400 or 15 : 28. Equating the profit ratio to the investment-time ratio gives (6000 * x) / (8000 * (x + 4)) = 15 / 28, which simplifies to 3x / (4x + 16) = 15 / 28. Solving 84x = 60x + 240 yields 24x = 240, so x equals 10.

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