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