A fruit seller buys some oranges at the rate of 4 for a rupee and an equal number at 5 for a rupee. He sells the whole lot at 9 for two rupees. Find his gain or loss per cent.
Given :
A fruit seller buys some oranges at the rate of 4 for a rupee and an equal number at 5 for a rupee. He sells the whole lot at 9 for two rupees.
To do :
We have to find the gain or loss per cent.
Solution :
Cost of 4 oranges$=Rs.\ 1$
The cost price of $x$ oranges $=Rs.\ \frac{1}{4}x$.
Cost of 5 oranges of the second variety$=Rs.\ 1$
The cost price of the second variety of $x$ oranges $=Rs.\ \frac{1}{5}x$.
The selling price of 9 oranges $=Rs.\ 2$
Total selling price of $2x$ oranges $=Rs.\ \frac{2}{9}\times2x = Rs.\ \frac{4x}{9}$
Total cost price of $2x$ oranges$=Rs.\ \frac{x}{4}+\frac{x}{5}$
$=Rs.\ \frac{5x+4x}{20}$
$=Rs.\ \frac{9x}{20}$
Loss $=$ Total cost price $-$ Total selling price
$=Rs.\ \frac{9x}{20}-\frac{4x}{9}$
$=Rs.\ \frac{81x-80x}{180}$
$=Rs.\ \frac{x}{180}$
Loss percent $=\frac{Loss}{Cost\ price} \times 100$
$ = \frac{\frac{x}{180}}{\frac{9x}{20}} \times 100$
$ = \frac{1}{81}\times100$
$ = 1.23$%.
Therefore, the loss % is 1.23%.
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