# Some toffees are bought at the rate of 11 for Rs 10 and the same number at the rate of 9 for Rs 10.

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.

Solution:

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 $1 \%$.

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