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Select the correct answerThe ratio of investment by A to that by B in a business is 14 :15 and the ratio of their respective profits at the end of a year is 2 : 5. If A invested the money for 3 months, then for how much time (in months) B invested his money?Options6597

Question

Select the correct answerThe ratio of investment by A to that by B in a business is 14 :15 and the ratio of their respective profits at the end of a year is 2 : 5. If A invested the money for 3 months, then for how much time (in months) B invested his money?Options6597

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Solution

Let's solve the problem step by step:

  1. Let's assume that A invested his money for 3 months.
  2. Since the ratio of investment by A to B is 14:15, we can assume that B invested his money for x months.
  3. Now, let's calculate the ratio of their respective profits. The ratio is given as 2:5.
  4. Since the profit is directly proportional to the time of investment, we can set up the following equation: (2/3) : (5/x) = 14 : 15.
  5. Cross-multiplying the equation, we get (2/3) * 15 = (5/x) * 14.
  6. Simplifying further, we have 10 = (70/x).
  7. Dividing both sides of the equation by 10, we get 1 = (7/x).
  8. Cross-multiplying again, we have x = 7.
  9. Therefore, B invested his money for 7 months.

So, the correct answer is 7.

This problem has been solved

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