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Mahesh purchased 10 kg of rice at the rate of ₹35 per kg and 38 kg of rice at ₹46 per kg. He sold the mixture at the rate of ₹43.5 per kg. Find his loss (in ₹).
10
5
18
15
10
Calculate the difference from the average: (35-43.5)10 + (46-43.5)38. This yields (-8.510) + (2.538) = -85 + 95 = +10. Since it's a profit calculation check, let's re-verify: CP = 350 + 1748 = 2098. SP = 48 * 43.5 = 2088. Loss = 2098 - 2088 = 10.
10 kg rice at ₹35/kg, 38 kg rice at ₹46/kg. Total quantity = 48 kg. Selling price (SP) = ₹43.5/kg.
Loss=Total Cost Price−Total Selling Price
Calculate the difference from the average: (35-43.5)10 + (46-43.5)38. This yields (-8.510) + (2.538) = -85 + 95 = +10. Since it's a profit calculation check, let's re-verify: CP = 350 + 1748 = 2098. SP = 48 * 43.5 = 2088. Loss = 2098 - 2088 = 10.
Students often miscalculate the total quantity or multiply the selling price by one of the quantities instead of the sum (48 kg).
Calculate Total Cost Price (CP)
Cost of 10 kg is 10×35=350 and cost of 38 kg is 38×46=1748. Total CP = 350+1748.
Total CP=350+1748=2098
Calculate Total Selling Price (SP)
Total quantity is 10+38=48 kg. Selling at 43.5 per kg, SP = 48×43.5.
Total SP=48×43.5=2088
Calculate Loss
Since CP > SP, there is a loss calculated by CP - SP.
Loss=2098−2088=10
A is correct because the total cost price is ₹2098 and the total selling price is ₹2088, resulting in a loss of ₹10.
This concept is foundational for 'Mixture and Alligation' problems, where calculating the mean price is essential to finding the ratio of quantities.
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