Incomes of A, B, and C are in the ratio 7 : 9 : 12 and their respective expenditures are in the ratio 8 : 9 : 15. If A saves 1 4 of his income, then the ratio of their savings is -

Answer: Option A

Let the incomes of A, B, C be 7x, 9x and 12x and their expenditures be 8y, 9y and 15y respectively
Then, A's saving = (7x - 8y)
$$\begin{array}{rl}& \therefore 7x-8y=\frac{1}{4}\text{of }7x\\ & \Rightarrow 8y=7x-\frac{7x}{4}\\ & \Rightarrow 8y=\frac{21}{4}x\\ & \Rightarrow y=\frac{21}{32}x\\ & \text{So, A’s expenditure}\\ & =\left(8\times \frac{21}{32}x\right)=\frac{168}{32}x\\ & \text{B’s expenditure}\\ & =\left(9\times \frac{21}{32}x\right)=\frac{189}{32}x\\ & \text{C’s expenditure}\\ & =\left(15\times \frac{21}{32}x\right)=\frac{315}{32}x\\ & \therefore \text{A’s saving}\\ & =\left(7x-\frac{168}{32}x\right)=\frac{56}{32}x\\ & \therefore \text{B’s saving}\\ & =\left(9x-\frac{189}{32}x\right)=\frac{99}{32}x\\ & \therefore \text{C’s saving}\\ & =\left(12x-\frac{315}{32}x\right)=\frac{69}{32}x\\ & \text{Hence, required ratio}\\ & =\frac{56}{32}x:\frac{99}{32}x:\frac{69}{32}x\\ & =56:99:69\end{array}$$