Question
The sum of the incomes of 'P', 'Q', 'R' together is Rs.
24000. 'P', 'Q' and 'R' spend 60%, 70%, and 65% of their respective incomes such that the ratio of their savings is 5:3:7, respectively. Find the sum of expenditures of 'P', 'Q', and 'R'.Solution
ATQ, Let the incomes of 'P', 'Q', and 'R' be Rs. p, Rs. q, and Rs. r. According to the question, 0.4p : 0.3q : 0.35r = 5 : 3 : 7 Or, p : q : r = (5/0.4) : (3/0.3) : (7/0.35) = 12.5 : 10 : 20 Sum of the ratios = 12.5 + 10 + 20 = 42.5 Therefore, income of ‘P’ = 24000 × (12.5/42.5) = Rs. 7059 Income of ‘Q’ = 24000 × (10/42.5) = Rs. 5647 Income of ‘R’ = 24000 - (7059 + 5647) = Rs. 11294 Required sum = (0.6 × 7059) + (0.7 × 5647) + (0.65 × 11294) = 4235 + 3953 + 7341 = Rs.15529
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