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