The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves 1/4 th of his income then the savings of A, B and C are in the ratio of = ?

Answer: Option A

Let income of A, B and C are 7x, 9x and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively
$$\begin{array}{rl}& \Rightarrow \text{Income}\text{of,}\\ & A\times \frac{1}{4}=\text{Saving}\text{of}\text{A}\left(\text{given}\right)\\ & \Rightarrow 7x-8y=7x\times \frac{1}{4}\\ & \Rightarrow 28x-32y=7x\\ & \Rightarrow 21x=32y\\ & \Rightarrow x:y=32:21\end{array}$$
∴ The ratio of savings of A, B and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69