Question
The total income of 'P' and 'Q' is Rs. 2,00,000. 'P'
spends 55% of his income, while 'Q' spends 80% of her income, such that the savings of 'Q' are Rs. 12,000 less than that of 'P'. If the income of 'R' is 30% more than the average savings of 'P' and 'Q' together, then find the savings of 'R', given that 'R' saves 30% of her income.Solution
Let the income of 'Q' be Rs. 'q'. Therefore, income of 'P' = Rs. (200000 - q). Savings of 'P' = 0.45 × (200000 - q). Savings of 'Q' = Rs. '0.2q'. According to the question, 0.45 * (200000 - q) = 0.2q + 12000 Or, 90000 – 0.45q = 0.2q + 12000 Or, 0.65q = 90000 - 12000 Or, q = 120000 Savings of 'P' = 0.45 × (200000 - q) = 90000 – 54000 = 36000 Savings of 'Q' = 24000 Therefore, income of 'R' = {36000 + 24000} ÷ 2 * 1.30 = 39000 Savings of 'Z' = 0.30 * 39000 = Rs. 11,700
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