The incomes of A, B and C are in the ratio 3 : 7 : 4 and their expenditures are in the ratio 4 : 3 : 5. If A saves \(14\frac{2}{7}\)% of his income, find the ratio of their savings.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 : 71 : 11
Saving = income − expenditure. The two ratios use different multipliers; A’s saving rate links them.
Incomes \(3x,\ 7x,\ 4x\); expenditures \(4y,\ 3y,\ 5y\)
\(\displaystyle 14\frac{2}{7}\%=\frac{1}{7}\), so A saves \(\displaystyle \frac{3x}{7}\)
\(\displaystyle 3x-4y=\frac{3x}{7}\), so \(\displaystyle 4y=\frac{18x}{7}\) and \(\displaystyle y=\frac{9x}{14}\)
Saving of A \(\displaystyle =\frac{3x}{7}=\frac{6x}{14}\)
Saving of B \(\displaystyle =7x-\frac{27x}{14}=\frac{71x}{14}\)
Saving of C \(\displaystyle =4x-\frac{45x}{14}=\frac{11x}{14}\)
Savings ratio \(=6:71:11\)
The ratio of their savings is 6 : 71 : 11.