Profit and Loss

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sukhman: Master | Next Rank: 500 Posts; Posts: 202; Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members; Thanked: 3 times

by sukhman » Sun Dec 20, 2015 5:23 am

If AJ sells an item at three-fourths of its selling price he incurs a loss of 4% . What will be the profit or loss percentage if he sells it at the actual selling price ?
a)30 b) 28 b) 14 c) 15 e)20

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Source: Beat The GMAT — Problem Solving | Sun Dec 20, 2015 5:23 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Dec 20, 2015 5:43 am

sukhman wrote:If AJ sells an item at three-fourths of its selling price he incurs a loss of 4% . What will be the profit or loss percentage if he sells it at the actual selling price ?
a)30 b) 28 b) 14 c) 15 e)20

Let the cost price = 100.

A loss of 4% = 100 - (4% of 100) = 100-4 = 96.

Let x = the selling price.
Since the $4 loss occurs if the product is sold at 3/4 of the selling price, we get:
96 = (3/4)x
32 = (1/4)x
x = 128.

Profit at the selling price = (selling price) - (cost price) = 128-100 = 28.
Profit percentage = profit/cost = 28/100 = 28%.

The correct answer is B.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Dec 21, 2015 3:19 am

sukhman wrote:If AJ sells an item at three-fourths of its selling price he incurs a loss of 4% . What will be the profit or loss percentage if he sells it at the actual selling price ?
a)30 b) 28 b) 14 c) 15 e)20

Let, three-fourths (3/4) of its selling price = 96
i.e. Selling Price = 96*(4/3) = 128

Also 96 = Cost price - 4% of cost price

i.e. 0.96*Cost price = 96

i.e. Cost price = 100

Profit or loss at actual SP = (SP - CP)*100/CP = [128-(100)]*100/(100) = 28% Profit

Answer: option B

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