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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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