Question

The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9: 15 If A saves $\frac{1}{4}th$ of his income then the savings of A, B and C are in the ratio

• A. 56 : 99 : 69
• B. 69 : 56 : 99
• C. 99 : 56 : 69
• D. 99 : 69 : 56

Answer 1

The correct option is A 56 : 99 : 69

Let the incomes of A,B and C be 7x, 9x and 12x respectively.
Let the expenditures of A,B and C be 8y, 9y and 15y respectively.
$\therefore$ Savinge of A,B and C are 7x-8y,9x-9y and 12x-15y respectively.
Given, $7x-8y=\frac{1}{4}\times 7x\Rightarrow 7x-\frac{7x}{4}=8y\Rightarrow \frac{21x}{4}=8y\Rightarrow y=\frac{21}{32}x\therefore$ Savings of A,B and C are
$\frac{7x}{4}:9x-\frac{9\times 21x}{32}:12x-15\times \frac{21x}{32}i.e.,\frac{7x}{4}:\frac{(288x-189x)}{32}:\frac{(384x-315x)}{32}\Rightarrow \frac{56}{32}:\frac{99x}{32}:\frac{69x}{32}\Rightarrow 56:99:69$