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Question

The profit percentage of the three articles A, B, and C is 10%, 20%, and 25% and the ratio of the cost price is 1 : 2: 4. Also, the ratio of the number of articles sold of A, B and C is 2: 5: 2. Then, the overall profit percentage is :

A
18.5%
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B
21%
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C
75%
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D
None of these
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Solution

The correct option is A 21%
Let CP of A, B, C be 100, 200, and 400 respectively.
Then profit for A, B, C = 10, 40, and 100 respectively.
Let the number of articles sold be 2, 5, 2 respectively for A, B, and C.
Total profit = 2×10+5×40+2×100=420
Total CP = 2×100+5×200+2×400=2000
Overall profit percentage = 4202000×100=21%.

Alternate Approach:
CP of A+B+C=2x×y+5x×2y+2x×4y=20xy
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total profit = 4.2xy
% profit =4.2xy20xy×100=21%

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