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.
Let the total number of toffees bought be $x$.
Let $\frac{x}{2}$ toffees at the rate of 11 are bought for Rs. 10, and $\frac{x}{2}$ toffees at the rate of 9 are bought for Rs. 10
Total money spent on buying the toffees $=\left(\frac{x}{2}\right)\left(\frac{10}{11}\right)+\left(\frac{x}{2}\right)\left(\frac{10}{9}\right)$
$=\frac{200 x}{198}$
$=\frac{100}{99} x$
It is given that $x$ toffees are sold at one rupee per toffee.
Therefore, the selling price of $x$ toffees $=$ Rs. $x \times 1=$ Rs. $x$
As $C . P$ is more than $S . P$, it will be $a$ loss.
Loss $=C . P-S . P$
$=\frac{100}{99} x-x$
$=\frac{100 x-99 x}{99}$
$=\frac{x}{99}$
Loss $\%=\frac{\text { Loss }}{C . P} \times 100$
$\frac{\frac{x}{99}}{\frac{100 x}{99}} \times 100=1 \%$
Total loss on the whole transaction would be $1 \%$.