Question

$X^{\prime }s$ salary is half that of $Y^{\prime }s$. If $X$ got a $50$ $\%$ rise in his salary and $Y$ got $25$ $\%$ rise in his salary, then the percentage increase in combined salaries of both is -

• A. $30$
• B. $33\frac{1}{3}$
• C. $37\frac{1}{2}$
• D. $75$

Answer 1

The correct option is B $33\frac{1}{3}$

Let the salary of $X$ be $x$ and the salary of $Y$ be $y$

Then $y=2x$ ....(1)

Their original combined salary $=x+y=x+2x=3x$ ....(by (1))

Increment in $X$'s salary $=x\times 50\%=x\times \frac{50}{100}=\frac{x}{2}$

Increment in $Y$'s salary $=y\times 25\%=y\times \frac{25}{100}=\frac{y}{4}$

$\therefore$new salary of $X=x+\frac{x}{2}=\frac{3x}{2}$ and new salary of $Y=y+\frac{y}{4}=\frac{5y}{4}$

Their new combined salary $=\frac{3x}{2}+\frac{5y}{4}=\frac{3x}{2}+\frac{5\left(2x\right)}{4}=4x$ (.....by (1))

Increment is $4x-3x=x$

$\therefore$ percentage of increment is $\frac{x}{3x}\times 100=33\frac{1}{3}\%$