Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
The incomes of $A, B$ and $C$ are in the ratio 7 : 10 : 12 and their expenses are in the ratio 8 : 10 : 15. If $A$ saves $\frac{1}{5}$ of his income, then $B^{\prime} s$ saving is what percent more or less than that of C's?
(a)100\% more
(b)$66 \frac{2}{3} \%$ more
(c)$33 \frac{1}{3} \%$ less
(d)40\% less
Answer
Answer (as printed): A
Explanation
Let the incomes of $A, B$ and $C$ be ₹ $7 x, ₹ 10 x$ and ₹ $12 x$ respectively and their expenses be ₹ $8 y$, ₹ $10 y$ and ₹ $15 y$ respectively. Then, $7 x-8 y=\frac{1}{5} \times 7 x$ $\Rightarrow 8 y=7 x-\frac{7 x}{5}=\frac{28 x}{5}$ $\Rightarrow 28 x=40 y \Rightarrow \frac{x}{y}=\frac{40}{28}=\frac{10}{7}$. Let $x=10 t$ and $y=7 t$.Then, $B$ 's saving $=₹(10 x-10 y)=₹[10(x-y)]$ $=₹[10(10 t-7 t)]=₹(30 t)$. C's saving $=₹(12 x-15 y)=₹(120 t-105 t)=₹(15 t)$. ∴ Required percentage $=\left(\frac{30 t-15 t}{15 t} \times 100\right) \%=100 \%$.
Explanation as extracted from the printed page; notation may be imperfect.