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Shopkeeper's Profit and Loss

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by anup.shesh » Thu Jul 21, 2011 10:24 pm
A shopkeeper sells an item at a profit of 6%. Had he sold at a loss of 2%, he would have earned $4 less. Find the selling price of the item.

(A) $49
(B) $50
(C) $52
(D) $53
(E) $106
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by knight247 » Thu Jul 21, 2011 10:40 pm
A few simple variations of the profit percent and loss percent formula

For Profit
SP=CP(1+P/100)

For Loss
SP=CP(1-L/100)

Where P is profit percent and L is loss percent

Using these formulas in our problem we get

SP1=CP(1+6/100)
SP1=1.06CP.....(1)

SP2=CP(1-2/100)
SP2=0.98CP

Cost price stays the same in both instances

Given that,
SP1-SP2=4
i.e. 1.06CP-0.98CP=4
CP=50....Substitute this value in (1)

SP=53 Hence, D
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by GMATGuruNY » Fri Jul 22, 2011 3:43 am
anup.shesh wrote:A shopkeeper sells an item at a profit of 6%. Had he sold at a loss of 2%, he would have earned $4 less. Find the selling price of the item.

(A) $49
(B) $50
(C) $52
(D) $53
(E) $106
The profit is 6%. The loss is 2%.
6% - (-2%) = 8%.
Thus, the difference between making a 6% profit and suffering a 2% loss -- $4 -- must be 8% of the cost.
4 = .08C
C = 4/.08 = 50.
Thus, the selling price = cost + 6% profit = 50 + .06*50 = 53.

The correct answer is D.
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