Question
P, Q, and R began a business with their investments in
the ratio 3:5:6. The profits were distributed in the ratio of 12:54:35 among P, R, and Q, respectively. Determine the ratio of the time periods for which P, Q, and R invested their money.Solution
Let the investment of 'P', 'Q' and 'R' be Rs. '3a', Rs. '5a' and Rs. '6a', respectively. Let the profit shares of 'P', 'Q' and 'R' be Rs. '12b', Rs. '35b' and Rs. '54b', respectively. Time period of investment of 'P' = (12b/3a) = (4b/a) Time period of investment of 'Q' = (35b/5a) = (7b/a) Time period of investment of 'R' = (54b/6a) = (9b/a) Therefore, required ratio = (4b/a) :(7b/a) :(9b/a) = 4:7:9
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