Discussion
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
Answer: D
Work back from the selling price to the cost of the mixture.
\[ \text{CP} = \frac{9.24}{1.10} = \text{Rs. } 8.40 \text{ per kg} \]
Let \( x \) kg of the Rs. 9 sugar be mixed with 27 kg of the Rs. 7 sugar:
\[ \frac{9x + 7(27)}{x + 27} = 8.40 \]
\[ 9x + 189 = 8.4x + 226.8 \quad\Longrightarrow\quad 0.6x = 37.8 \]
\[ x = 63 \text{ kg} \]
The gain is stated on the mixture, so the selling price must be converted to a cost price before any mixing calculation.
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