The ratio of selling price of article $A, B, C$ is $8 : 9 : 5$ and ratio of percentage profit is $8 : 7 : 14$ respectively. If the profit percentage of $A$ is $14.28\%$ and the cost price of $B$ is Rs. $400$. What is the overall percentage gain?
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$14.87\ %$
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$16.66\ %$
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$14.28 \%$
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$15.78 \%$
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None of these
D
Correct answer
Explanation
SP ratio A:B:C = 8:9:5. Profit % ratio A:B:C = 8:7:14. Profit % A = 14.28% = 1/7. Since 8 units = 1/7, 1 unit = 1/56. Profit % B = 7 * (1/56) = 1/8 = 12.5%. Profit % C = 14 * (1/56) = 1/4 = 25%. CP of B = 400. SP of B = 400 * 1.125 = 450. Since SP ratio is 8:9:5, 9 units = 450, 1 unit = 50. SP A = 400, SP C = 250. CP A = 400 / (8/7) = 350. CP C = 250 / 1.25 = 200. Total CP = 350+400+200 = 950. Total SP = 400+450+250 = 1100. Gain = 150/950 = 15.78%.