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P and Q invested some money in a business in the ratio of 4 : 7 respectively. After 6 months P withdraws his capital. If they receive profits in the ratio of 4 : 21, then for how many months did Q invest in the business?

P and Q invested some money in a business in the ratio of 4 : 7 respectively. After 6 months P withdraws his capital. If they receive profits in the ratio of 4 : 21, then for how many months did Q invest in the business? Correct Answer 18

Let Q invested his money of t months and amount of P and Q are 4a and 7a.

Ratio of profit = P’s capital × time : Q’s capital × time

⇒ 4 : 21 = 4a × 6 : 7a × t

⇒ 4 : 21 = 24 : 7t

⇒ 4/21 = 24/7t

∴ t = 18 months

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