Question

# By selling an item for Rs. 24, the shopkeeper earns the percentage profit equal to cost price of the item. Find the cost price.

A

120

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B

-120

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C

-20

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D

20

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Solution

## The correct option is D 20 Let the cost price be x Profit on the item is 24−x Profit % = S.P−C.PC.P×100 =24−xx×100 Given that the profit percentage is equal to the cost price. ⇒24−xx×100=x ⇒x2=2400−100x ⇒x2−2400+100x=0 ⇒x2+120x−20x−2400=0 ⇒(x+120)(x−20)=0 ⇒x=−120 or 20 Cost price of an item cannot be negative. So, the cost price is Rs. 20

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