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

Answer: (B)

$50$

Let number of pens be $x$

Hence, number of pencils will be $\frac{3}{2}x$

Cost of one pen is $Rs.5$

Hence, total C.P. of pens $=5x$

Also, cost of one pencil is $Rs.1$

Hence, total C.P. of pencils $=\frac{3}{2}x$

It is also given that, pens are sold at $12\%$ profit,

Hence, $S.P.=112\%of5x$

$=\frac{112}{100}\times 5x$

$=\frac{28x}{5}$

Also, pencils are sold at $10\%$ profit,

Hence, $S.P.=110\%of\frac{3}{2}x$

$=\frac{330}{200}x$

$=\frac{33x}{20}$

Now, total sale is $Rs.725$.

Hence, $\frac{28x}{5}+\frac{33x}{20}=725$

$112x+33x=725\times 20$

$145x=14500$

$x=100$
Thus, number of pens $=100$

Number of pencils $=\frac{3}{2}\times 100$

$=150$

So, the number of pencils exceeds the number of pens by $50$.

Hence, option B is correct.