Question
Download Solution PDFHow much wheat (in kg, rounded off to the nearest integer) costing ₹36 per kg must be mixed with 55 kg of wheat costing ₹45 per kg so that there may be a gain of 20% by selling the mixture at ₹50 per kg?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Cost of wheat A = ₹36 per kg
Cost of wheat B = ₹45 per kg
Quantity of wheat B = 55 kg
Selling price of the mixture = ₹50 per kg
Desired profit = 20%
Calculation:
Let the quantity of wheat A to be mixed = x kg
Cost of the mixture = (Cost of wheat A × Quantity of A) + (Cost of wheat B × Quantity of B)
Total cost = 36x + 45 × 55
Total quantity = x + 55
Desired selling price = Cost price × (1 + Profit%)
50 × (x + 55) = (36x + 45 × 55) × (1 + 20 / 100)
50 × (x + 55) = 1.2 × (36x + 45 × 55)
50x + 50 × 55 = 1.2 × (36x + 45 × 55)
50x + 2750 = 1.2 × (36x + 2475)
50x + 2750 = 43.2x + 2970
50x − 43.2x = 2970 − 2750
6.8x = 220
x = 220 / 6.8 = 32.35 kg
∴ The quantity of wheat A required is approximately 32 kg (rounded to the nearest integer).
Last updated on Jun 2, 2025
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