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7.Profit and Loss
hard
A shopkeeper sold two bicycles for $Rs.\,1500$ each. On one, he gains $25 \%$ and on the other he loses $20 \%$. His gain or loss per cent in the whole transaction is
A
$2 \frac{18}{41} \%$ loss
B
$2 \frac{18}{41} \%$ gain
C
$2 \%$ gain
D
None of these
Solution
Here $x=25$ and $y=-20$
$\therefore \quad$ Overall gain$/$loss $\%$
$=\left[\frac{100(x+y)+2 x y}{(100+x)+(100+y)}\right] \%$
$=\left[\frac{100(25-20)+2 \times 25 \times-20}{(100+25)+(100-20)}\right] \%$
$=-\frac{100}{41} \%$ or $-2 \frac{18}{41} \%$
which represents loss being $a -ve$ expression.
Standard 13
Quantitative Aptitude
