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- Standard 13
- Quantitative Aptitude
A shopkeeper listed the price of goods at $30 \%$ above the cost price. He sells half the stock at this price, one fourth of the stock at a discount of $15 \%$ and the remaining at $30 \%$ discount. His overall profit is.......$\%$
$15 \frac{3}{8}$
$15$
$-15 \frac{3}{5}$
$15 \frac{2}{3}$
Solution
Let the number of items $=4$
$C.P.$ of each $=100 x$
Mark$-$up $=30 \%(100 x)=30 x$
$M.P.$ $=100 x+3 x=130 x$
$\therefore$ $S.P.$ of first $2$ items $2$ box
For first $2$ items, $S.P. =130 x \times 2=260 x$
$3^{\text {rd }}$ item, discount $=15 \%=15 \%(130 x)=19.5 x$
$\therefore$ $S.P.$ of $3^{\text {rd }}$ item $=130 x-19.5 x=110.5 x$
Discount for last item $=30 \%(130 x)=39 x$
$S.P.$ of last item $=130 x-39 x=91 x$
Total $S.P.$ $=260 x+110.5 x+91 x=461.5 x$
Total $CP .=400 x$
Profit $\%=\frac{461.5 x-400 x}{400 x} \times 100=\frac{123}{8}=15\frac{3}{8} \%$
