Question : How many kilograms of rice costing INR 52 per kg must be mixed with 35 kg of rice costing INR 45 per kg to get a gain of 10% by selling the resulting mixture of rice at the rate of INR 55 per kg?
Option 1: 87.5 kg
Option 2: 90.0 kg
Option 3: 85.0 kg
Option 4: 82.5 kg
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Correct Answer: 87.5 kg
Solution :
Gain% = 10%
The selling price of the mixture = INR 55
Amount of rice costing INR 45 per kg = 35 kg
Let the quantity of rice costing Rs. 42 per kg be $x$ kg
The cost price of the mixture = Rs. $\frac{55}{110}$ × 100 = Rs. 50 per kg
Equating cost price of mixture weighing (x + 35) kg,
50 × ($x$ + 35) = 52 × $x$ + 35 × 45
⇒ 35 × 5 = 2$x$
⇒ $x$ = 87.5 kg
Hence, the correct answer is 87.5 kg.
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