# How much percent above the cost prize should a shopkeeper mark his goods so that even after allowing a discount of 20%, he still gains 10%?

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by sahbahasan

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by sahbahasan

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Let the shopkeeper mark the prices at x% higher than cost price CP.

Let MP = (100+x)/100 * CP

Price after discount = 80% MP = 80(100+x) CP /10,000

sale price with a gain of 10% = 110 % CP

Hence : 110 CP/100 = 80 (100+x) CP / 10, 000

100 +x = 110 * 100 / 80 = 137.5

x = 37.5 => Marking price is 37.5 % above cost price.

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alternately

let the cost price be Rs 100.

MP = 100 + x

Price after discount = (100 + x) * 80/100

Sale price with 10% gain = CP + 10% CP = 100 + 10 = Rs 110

Hence (100 + x) 8/10 = 110 => 100 + x = 1100/8 = 137.5

x = 37.5 %

Let MP = (100+x)/100 * CP

Price after discount = 80% MP = 80(100+x) CP /10,000

sale price with a gain of 10% = 110 % CP

Hence : 110 CP/100 = 80 (100+x) CP / 10, 000

100 +x = 110 * 100 / 80 = 137.5

x = 37.5 => Marking price is 37.5 % above cost price.

==============================

alternately

let the cost price be Rs 100.

MP = 100 + x

Price after discount = (100 + x) * 80/100

Sale price with 10% gain = CP + 10% CP = 100 + 10 = Rs 110

Hence (100 + x) 8/10 = 110 => 100 + x = 1100/8 = 137.5

x = 37.5 %