Question

Some toffees are bought at the rate of $11$ for $Rs.10$ and the same number at the rate of $9$ for $Rs.10$. If the whole lot is sold at one rupee per toffee, find the gain or loss percent on the whole transaction.

Answer 1

In first condition:
CP of $11$ toffees $=Rs.10$
Thus, the CP of $1$ toffee $=Rs.\frac{10}{11}$
In second condition:
CP of $9$ toffees $=Rs.10$
CP of $1$ toffees $=Rs.\frac{10}{9}$
Total CP for both toffees$=Rs.\frac{10}{11}+\frac{10}{9}$

$=\frac{90+110}{99}$

$=Rs.\frac{200}{99}$

CP of $1$ toffee $=\frac{200}{99\times 2}=\frac{100}{99}$

Given SP of $1$ toffee $=Rs.1$

Since CP$>$SP

So, loss amount$=$CP$-$SP

$=\frac{100}{99}-1$

$=\frac{100-99}{99}$

$=Rs.\frac{1}{99}$

Thus, the loss percent$=\frac{\text{loss}}{\text{CP}}\times 100$

$=\frac{\frac{1}{99}}{\frac{100}{99}}\times 100\%$

$=\frac{1}{99}\times \frac{99}{100}\times 100\%$

$=1\%$