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      Question

      The incomes of P, Q and R are in the ratio 10 : 12 : 9

      and their expenditures are in the ratio 12 : 15 : 8. If Q saves 25% of his income, then what is the ratio of the savings of P, Q and R?
      A 15 : 14 : 21 Correct Answer Incorrect Answer
      B 14 : 15 : 21 Correct Answer Incorrect Answer
      C 21 : 15 : 14 Correct Answer Incorrect Answer
      D 21 : 14 : 15 Correct Answer Incorrect Answer

      Solution

      Income Ratio (P:Q:R) = 10:12:9 Let incomes be 10x, 12x, 9x. Expenditure Ratio (P:Q:R) = 12:15:8 Let expenditures be 12y, 15y, 8y. Q saves 25% of income: Savings of Q = 25% of 12x = 3x Expenditure of Q = 12x - 3x = 9x 15y = 9x ⟹y = 3x/5 Expenditures: P = 12 × 3x/5 = 36x/5  R = 8 × 3x/5 = 24x/5  Savings: P= 10x – 36x/5 =14x/5 R = 9x − 24x/ 5 = 21x/5  Savings Ratio (P:Q:R) = 14:15:21

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