Question

X buys pens and pencils at $Rs.5$ and $Rs.1$ per piece respectively. For every two pens, he buys three pencils. He sold pens and pencils at $12\%$ and $10\%$ profit respectively. If his total sale is $Rs.725$, then the number of pencils exceeds the number of pens by:

• A. $25$
• B. $50$
• C. $75$
• D. $90$

Answer 1

The correct option is B $50$

It is given that, for every $2$ pens, he buys $3$ pencils.

Let number of pens $=2x$

and number of pencils $=3x$

Cost price of $2x$ pencils $=Rs.2x\times 5=Rs.10x$............(i)

Cost price of $3x$ pencils $=Rs.3x\times 1=Rs.3x$ .............(ii)

S.P. of $2x$ pens $=Rs.(10x+12\%of10x)$

$=Rs.10x(1+12\%)$

$=Rs.10x\left(1.12\right)$

$=Rs.11.20x$ ...........(iii)

S.P. of $3x$ pencils $=Rs.(3x+10\%of3x)$

$=Rs.3x(1+10\%)$

$=Rs.3x\left(1.10\right)$

$=Rs.3.30x$..........(iv)

Total S.P. $=Rs.(11.20x+3.30x)=Rs.14.50x$

$\therefore$ $14.50x=725$

$⟹x=\frac{725}{14.50}$

$⟹x=50$

Number of Pens $=2x=2\times 50=100$

Number of Pencils $=3x=3\times 50=150$

Hence, number of pencils exceeds the number of pen by $150-100=50$.