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The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?

Correct answer: B. 10 months

  • A. 7 months
  • B. 10 months
  • C. 9 months
  • D. 11 months

Explanation

Profit is proportional to investment multiplied by time. P's investment-time is 7 x 5 = 35 units and Q's is 5 x t units; because the profit ratio is 7:10, 35:5t = 7:10, giving t = 10 months. Option a is a likely choice from assuming equal investment periods.

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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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