Question

The ratio of the incomes of $P$ and $Q$ is $5: 4$. The ratio of their expenditure is $4: 3$. The savings of $P$ is more than that of $Q$ by $16 \frac{2}{3} \%$. What percentage of his income does $P$ spend?

• A. $52 \frac{2}{3} \%$
• B. $53 \frac{1}{3} \%$
• C. $54 \frac{1}{3} \%$
• D. $51 \frac{2}{3} \%$

Answer 1

Answer: (B)

Let the incomes of $P$ and $Q$ be $₹ 5 x$ and $₹ 4 x$, respectively. Let the expenditure of $P$ and $Q$ be $₹ 4 y$ and $₹ 3 y$, respectively.
Savings of $P=₹(5 x-4 \gamma)$
Savings of $Q=₹(4 x-3 y)$
$\therefore 5 x-4 y=(4 x-3 y)(\frac{16 \frac{2}{3}}{100}) $
$\Rightarrow 5 x-4 y=(4 x-3 y)(\frac{7}{6}) $
$\Rightarrow 30 x-24 y=28 x-21 y$
$\Rightarrow 2 x=3 y $
$\text { Required percentage }=\frac{4 y}{5 x}(100) $
$=\frac{4}{5}(\frac{2}{3})(100)=53 \frac{1}{3} \%$