Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2009 · Marks: · Difficulty:
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 $\frac{1}{4}$ of his income, then the ratio of their savings is
(a)56 : 99 : 69
(b)33 : 19 : 23
(c)15 : 28 : 27
(d)56 : 69 : 99
Answer
Answer (as printed): A
Explanation
Let the incomes of $A, B, C$ be $7 x, 9 x$ and $12 x$ and their expenditures be $8 y, 9 y$ and $15 y$ respectively. Then, $A$ 's saving $=(7 x-8 y)$. $\therefore 7 x-8 y=\frac{1}{4}$ of $7 x \Rightarrow 8 y=7 x-\frac{7 x}{4} \Rightarrow 8 y=\frac{21}{4} x$ $\Rightarrow y=\frac{21}{32} x$. So, $A$ 's expenditure $=\left(8 \times \frac{21}{32} x\right)=\frac{168}{32} x$; B's expenditure $=\left(9 \times \frac{21}{32} x\right)=\frac{189}{32} x$; C's expenditure $=\left(15 \times \frac{21}{32} x\right)=\frac{315}{32} x$. ∴ A's saving $=\left(7 x-\frac{168}{32} x\right)=\frac{56}{32} x$; B's saving $=\left(9 x-\frac{189}{32} x\right)=\frac{99}{32} x$; C's saving $=\left(12 x-\frac{315}{32} x\right)=\frac{69}{32} x$. Hence, required ratio $=\frac{56}{32} x: \frac{99}{32} x: \frac{69}{32} x=56: 99: 69$.
Explanation as extracted from the printed page; notation may be imperfect.