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The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income,what is the ratio of the savings of P, Q and R ?15 : 8 : 219 : 7 : 97 : 15 : 107 : 15 : 10

Question

The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income,what is the ratio of the savings of P, Q and R ?15 : 8 : 219 : 7 : 97 : 15 : 107 : 15 : 10

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Solution

Let's solve this step by step:

Step 1: Let's assume the incomes of P, Q, and R as 6x, 8x, and 11x respectively. Similarly, let's assume the expenditures of P, Q, and R as 5y, 8y, and 12y respectively.

Step 2: It's given that P saves 1/4th of his income. So, the savings of P = Income of P - Expenditure of P = 6x - 5y.

Step 3: But we know that the savings of P is 1/4th of his income. So, 1/4 * 6x = 6x - 5y. Solving this equation, we get y = x/2.

Step 4: Now, let's find the savings of Q and R. The savings of Q = Income of Q - Expenditure of Q = 8x - 8y = 8x - 8*(x/2) = 4x. Similarly, the savings of R = Income of R - Expenditure of R = 11x - 12y = 11x - 12*(x/2) = 5x.

Step 5: Therefore, the ratio of the savings of P, Q, and R = 6x : 4x : 5x = 6 : 4 : 5.

So, the ratio of the savings of P, Q, and R is 6 : 4 : 5.

This problem has been solved

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