The incomes of A, B and C are in the ratio 2 : 5 : 3 and their expenditures are in the ratio 3 : 4 : 2. If A saves 25% of his income, find the ratio of their savings.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 6 : 4
Saving = income − expenditure. The two ratios use different multipliers; A’s saving rate links them.
Incomes \(2x,\ 5x,\ 3x\); expenditures \(3y,\ 4y,\ 2y\)
\(\displaystyle 25\%=\frac{1}{4}\), so A saves \(\displaystyle \frac{2x}{4}=\frac{x}{2}\)
\(\displaystyle 2x-3y=\frac{x}{2}\), so \(\displaystyle 3y=\frac{3x}{2}\) and \(\displaystyle y=\frac{x}{2}\)
Saving of A \(\displaystyle =\frac{x}{2}\)
Saving of B \(=5x-2x=3x\)
Saving of C \(=3x-x=2x\)
Savings ratio \(\displaystyle =\frac{x}{2}:3x:2x=1:6:4\)
The ratio of their savings is 1 : 6 : 4.