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 $$\frac{{\text{1}}}{{\text{4}}}$$ of his income, then the ratio of their savings is -

Solution(By Examveda Team)

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)
$$\eqalign{ & \therefore 7x - 8y = \frac{1}{4}{\text{of }}7x \cr & \Rightarrow 8y = 7x - \frac{{7x}}{4} \cr & \Rightarrow 8y = \frac{{21}}{4}x \cr & \Rightarrow y = \frac{{21}}{{32}}x \cr & {\text{So, A's expenditure}} \cr & = \left( {8 \times \frac{{21}}{{32}}x} \right) = \frac{{168}}{{32}}x \cr & {\text{B's expenditure}} \cr & = \left( {9 \times \frac{{21}}{{32}}x} \right) = \frac{{189}}{{32}}x \cr & {\text{C's expenditure}} \cr & = \left( {15 \times \frac{{21}}{{32}}x} \right) = \frac{{315}}{{32}}x \cr & \therefore {\text{A's saving}} \cr & = \left( {7x - \frac{{168}}{{32}}x} \right) = \frac{{56}}{{32}}x \cr & \therefore {\text{B's saving}} \cr & = \left( {9x - \frac{{189}}{{32}}x} \right) = \frac{{99}}{{32}}x \cr & \therefore {\text{C's saving}} \cr & = \left( {12x - \frac{{315}}{{32}}x} \right) = \frac{{69}}{{32}}x \cr & {\text{Hence, required ratio}} \cr & = \frac{{56}}{{32}}x:\frac{{99}}{{32}}x:\frac{{69}}{{32}}x \cr & = 56:99:69 \cr} $$