Question

A shopkeeper sold one fourth of his goods at a loss of $10\%$. He sold the remaining at a higher percent of profit to get $12\frac{1}{2}$% profit on the whole transaction. The higher profit percent is

• A. $17\frac{1}{2}$%
• B. $33\frac{1}{3}$%
• C. $22\frac{1}{2}$%
• D. $20\%$

Answer 1

The correct option is D $20\%$

Let C.P. = Rs.c

$\therefore$ C.P. of $\frac{1}{4}$th of the goods = Rs.$\frac{c}{4}$

Loss = 10%
$\therefore$ S.P. of $\frac{1}{4}$th of the goods $=\frac{\frac{c}{4}\times 90}{100}=Rs.\frac{9c}{40}$
C.P. of $\frac{3}{4}$th of the goods = RS.$\frac{3c}{4}$

Let profit on this remaining part = P% Then
S.P. of $\frac{3}{4}th$ of the goods = $\frac{\frac{3c}{4}\times (100+P)}{100}=\frac{3c}{400}(100+P)$
Profit on the whole transaction = 12.5%

$\therefore$ S.P. of the whole =Rs.$\frac{c\times 112.5}{100}$
$\therefore$ $\frac{9c}{40}+\frac{3c}{4}+\frac{3c\times P}{400}=\frac{112.5c}{100}$
$\Rightarrow \frac{90+300+3P}{400}=\frac{112.5}{100}$
$\Rightarrow \frac{390+3P}{4}=112.5\Rightarrow 390+3P=450\Rightarrow 3P=60\Rightarrow P=20$