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Amit purchased 10 kg of rice at the rate of ₹35 per kg and 39 kg of rice at ₹44 per kg. He sold the mixture at the rate of ₹42 per kg. Find his loss (in ₹).
8
3
13
16
8
Calculate individual total costs (350 + 1716 = 2066) and compare with total revenue (49 * 42 = 2058). The difference is the loss.
10 kg of rice at ₹35/kg and 39 kg of rice at ₹44/kg. Sold 49 kg of mixture at ₹42/kg.
Loss=Cost Price−Selling Price
Calculate individual total costs (350 + 1716 = 2066) and compare with total revenue (49 * 42 = 2058). The difference is the loss.
Many students miscalculate 39×44 as 1706 or 1726 instead of 1716, leading to wrong loss values.
Calculate Total Cost Price (CP)
Find cost of both rice varieties: 10×35=350 and 39×44=1716. Total CP=350+1716=2066.
CP=350+1716=2066
Calculate Total Selling Price (SP)
Total quantity is 10+39=49 kg. Selling price per kg is 42. Total SP=49×42=2058.
SP=49×42=2058
Calculate Loss
Since CP>SP, there is a loss: Loss=CP−SP=2066−2058=8.
Loss=2066−2058=8
A is correct because the total cost price is ₹2066 and the total selling price is ₹2058, resulting in a loss of ₹8.
This concept of 'Weighted Average' is frequently used in mixtures and alligations to find the mean price of a commodity blend.
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