A trader mixes three varieties of groundnuts costing Rs. 50, Rs. 20 and Rs. 30 per kg in the ratio 2 : 4 : 3 in terms of weight, and sells the mixture at Rs. 33 per kg. What percentage of profit does he make?
- Suppose he bought 2 kg, 4 kg and 3 kg of the three varieties.
C.P. of 9 kg = Rs. (2 x 50 + 4 x 20 + 3 x 30) = Rs. 270
S.P. of 9 kg = Rs. (9 x 33) = Rs. 297
Profit% = 27 270 x 100 % = 10%
Let's assume that the trader mixes 2x kg of the first variety, 4x kg of the second variety, and 3x kg of the third variety.
Then the total cost price (CP) of the mixture is:
CP = (502x + 204x + 30*3x) = 100x + 80x + 90x = 270x
And the total weight of the mixture is:
2x + 4x + 3x = 9x
Therefore, the cost price per kg of the mixture is:
CP per kg = CP / (9x) = 270x / (9x) = Rs. 30
The trader sells the mixture at Rs. 33 per kg, so his selling price (SP) is:
SP per kg = Rs. 33
Therefore, the profit per kg of the mixture is:
Profit per kg = SP per kg - CP per kg = Rs. 33 - Rs. 30 = Rs. 3
And the percentage profit is:
Percentage profit = (Profit per kg / CP per kg) x 100% = (3/30) x 100% = 10%
Therefore, the answer is option C: 10%.
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