How many kilograms of wheat costing Rs.8 per kg 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?
Question
How many kilograms of wheat costing Rs.8 per kg 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?
Solution
Sure, let's solve this step by step.
Step 1: Let's assume the quantity of wheat to be mixed is 'x' kg.
Step 2: The cost price of the wheat is Rs.8 per kg. So, the total cost of the wheat is 8x.
Step 3: The cost price of the rice is Rs.5.40 per kg. So, the total cost of the rice is 5.40 * 36 = Rs.194.40.
Step 4: The total cost price of the mixture is the sum of the cost of the wheat and the rice, which is 8x + 194.40.
Step 5: The selling price of the mixture is Rs.7.20 per kg. So, the total selling price for (x + 36) kg is 7.20 * (x + 36).
Step 6: According to the problem, there is a 20% gain. This means the total selling price is 120% of the total cost price. So, we can set up the equation: 7.20 * (x + 36) = 1.20 * (8x + 194.40).
Step 7: Solve this equation to find the value of 'x'.
7.20x + 259.20 = 9.60x + 233.28
Subtract 7.20x from both sides:
259.20 - 233.28 = 9.60x - 7.20x
25.92 = 2.40x
Divide by 2.40:
x = 25.92 / 2.40
x = 10.8
So, 10.8 kg of wheat must be mixed with the 36 kg of rice.
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