How many kg of wheat costing R8 must be mixed with 36 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg? Options : 10kg 12kg 9.8kg 10.8kg
Question
How many kg of wheat costing R8 must be mixed with 36 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?
Options : 10kg 12kg 9.8kg 10.8kg
Solution
Let's denote the amount of wheat to be mixed as 'x' kg.
The cost price of the wheat is Rs. 8 per kg, so the total cost of the wheat is 8x.
The cost price of the rice is Rs. 5.40 per kg, so the total cost of the rice is 5.4 * 36 = Rs. 194.4.
The total cost of the mixture is therefore 8x + 194.4.
The selling price of the mixture is Rs. 7.20 per kg, and we want a 20% gain. This means the cost price of the mixture should be 80% of the selling price.
Therefore, we can set up the following equation:
8x + 194.4 = 0.8 * 7.2 * (x + 36)
Solving this equation for 'x' will give us the amount of wheat to be mixed.
8x + 194.4 = 5.76x + 207.36
Subtract 5.76x from both sides:
2.24x = 12.96
Finally, divide both sides by 2.24 to solve for 'x':
x = 12.96 / 2.24
x ≈ 5.8 kg
However, this is not an option in the given choices. It seems there might be a mistake in the problem or the options provided.
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