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P, Q and R started a business. P invests money for 6 months & claims 1/4th of the total profit, Q invests money for 3 months and claims 1/6th of the profit while R invests Rs. 14700 for 8 months. How much money P and Q invested together?

P, Q and R started a business. P invests money for 6 months & claims 1/4th of the total profit, Q invests money for 3 months and claims 1/6th of the profit while R invests Rs. 14700 for 8 months. How much money P and Q invested together? Correct Answer Rs. 19600

Since P claims 1/4th profit and Q claims 1/6th profit:

∴ Profit share of R = 1 - 1/4 - 1/6 = 14/24th of total profit

∴ Ratio of profit sharing = 1/4 : 1/6 : 14/24 = 6 : 4 : 14 = 3 : 2 : 7

Ratio of time for which they invested = 6 : 3 : 8

∴ Ratio of investment = (3/6) : (2/3) : (7/8) = 12 : 16 : 21

Since R invests Rs. 14700;

∴ Amount invested by (P + Q) = × 14700

⇒ 28 × 700 = Rs. 19600

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