Multiple choice

In what ratio did A, B and C invest money in the business, if they were partners in the business for 18 months, 15 months and 12 months, respectively. Also, they shared the profit of the business in the ratio 6 : 8 : 10.

  1. 10 : 16 : 25

  2. 20 : 52 : 75

  3. 37 : 51 : 72

  4. 41 : 49 : 65

  5. 42 : 49 : 60
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A Correct answer
Explanation

Profit ratio = (Investment * Time). Let investments be I_A, I_B, I_C. 18*I_A : 15*I_B : 12*I_C = 6 : 8 : 10. I_A = 6/18 = 1/3. I_B = 8/15. I_C = 10/12 = 5/6. Ratio = 1/3 : 8/15 : 5/6 = 10 : 16 : 25.

AI explanation

Using the basic partnership formula, the ratio of profit is equal to the product of the investment ratio and the time period. Let the investment ratio be I and the time ratio be 18:15:12, which simplifies to 6:5:4. The profit ratio is given as 6:8:10, which simplifies to 3:4:5, so the equation becomes I * (6:5:4) = (3:4:5). By dividing the profit ratio parts by the corresponding time ratio parts, the investment ratio is 3/6 : 4/5 : 5/4, which simplifies to 10:16:25.

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