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# A shoe shop owner lists the price of a pair of shoes as the price

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Current Student
Joined: 27 May 2014
Posts: 525
GMAT 1: 730 Q49 V41
A shoe shop owner lists the price of a pair of shoes as the price  [#permalink]

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30 May 2018, 23:08
2
00:00

Difficulty:

65% (hard)

Question Stats:

37% (01:34) correct 63% (01:31) wrong based on 38 sessions

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A shoe shop owner lists the price of a pair of shoes as the price at which he purchased the pair from the manufacturer plus a markup which is equal to 40 percent of the selling price. After some time, he offers a discount on the shoes which is equal to 20 percent of the selling price. Which of the following best represents the profit, as a percentage of the purchase price, which he earns on selling the pair of shoes?

A. 11%
B. 12%
C. 17%
D. 20%
E. 25%

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Joined: 04 Jan 2015
Posts: 2438
Re: A shoe shop owner lists the price of a pair of shoes as the price  [#permalink]

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30 May 2018, 23:36
1
1

Solution

Given:
• List price = purchase price + mark-up = cost price + 40% of selling price
• Discount = 20% of the selling price

To find:
• Profit, as a percentage of the purchase (cost) price

Approach and Working:
Let us assume the cost price to be c and selling price to be x
• List price = c + $$\frac{2x}{5}$$

On the list price, discount given = 20% of selling price = $$\frac{x}{5}$$
• Hence, selling price after discount = $$c + \frac{2x}{5} – \frac{x}{5} = c + \frac{x}{5}$$
Now, as we assumed the selling price to be x, we can say $$x = c + \frac{x}{5}$$
Or, $$c = \frac{4x}{5}$$
Hence, profit percentage = (x – $$\frac{4x}{5}$$)/($$\frac{4x}{5}$$) * 100 = 25%

Hence, the correct answer is option E.

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Joined: 04 Apr 2018
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GMAT 1: 710 Q50 V37
Re: A shoe shop owner lists the price of a pair of shoes as the price  [#permalink]

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31 May 2018, 08:06
EgmatQuantExpert wrote:

Solution

Given:
• List price = purchase price + mark-up = cost price + 40% of selling price
• Discount = 20% of the selling price

To find:
• Profit, as a percentage of the purchase (cost) price

Approach and Working:
Let us assume the cost price to be c and selling price to be x
• List price = c + $$\frac{2x}{5}$$

On the list price, discount given = 20% of selling price = $$\frac{x}{5}$$
• Hence, selling price after discount = $$c + \frac{2x}{5} – \frac{x}{5} = c + \frac{x}{5}$$
Now, as we assumed the selling price to be x, we can say $$x = c + \frac{x}{5}$$
Or, $$c = \frac{4x}{5}$$
Hence, profit percentage = (x – $$\frac{4x}{5}$$)/($$\frac{4x}{5}$$) * 100 = 25%

Hence, the correct answer is option E.

I am a bit confused as to the question and the solution provided.

Using picking number strategy.

Given:
• List price = purchase price + mark-up = cost price + 40% of selling price
• Discount = 20% of the selling price

To find:
• Profit, as a percentage of the purchase (cost) price

Approach and Working:
Lets assume list price is $10. • List price = cost price + 40% of selling price$10 = $6 +$4
But with a 20% discount, a ($2) discount, the new formula should be • Old List price - Discount = cost price + 40% of selling price - discount$10 - $2 =$6 + $4 -$2
• Since the discount is coming from the shop owner's pocket, it should come from his profit
$8 =$6 + $2 Should the new list price be$8, and the cost price and profit be be $6 and$2 respectively?

From EgmatQuantExpert solution provided, it seems that not only does the List Price not change, but the cost price went up also? Not sure why the owner providing the discount will lead the manufacturer to raise the cost price
• List price = cost price + 40% of selling price
$10 =$6 + $4 But with a 20% discount, a ($2) discount, the new formula should be
• List price = cost price + 40% of selling price - discount
$10 =$C + $4 -$2
$10 =$C + $2$C = $10 -$2

I dont think any where in the question does it mention that Selling Price remains constant despite providing a discount, and the cost change as a result.

Please let me know where the logic gap is.
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Joined: 04 Jan 2015
Posts: 2438
Re: A shoe shop owner lists the price of a pair of shoes as the price  [#permalink]

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01 Jun 2018, 05:29
1
fusion327 wrote:

Please let me know where the logic gap is.

Hi,
There are certain cases where you implemented the theory incorrectly.

1. You mentioned List price = cost price + 40% of selling price
Which is 10 = 6 + 4
Now, if 4 denotes 40% of the selling price, then you must have assumed selling price to be 10, but actually you have assumed list price as 10.

2. The whole question data is provided with fixed value of all the elements – cost price, selling price, and list price. If the values of these elements change every time, then there is no way one can apply the logic of profit or loss percentage as every set of different values will give us different profit or loss percentage.

3. When you calculate the list price, you should only consider the initial cost price and the mark-up value but not the discount amount. Unless specified otherwise, by default discount is given on the basis of list price.
List price = cost price + mark-up value
Discount percentage = percentage of less of the list price

4. As per the question,
• Cost price = $$\frac{4x}{5}$$
• Selling price = x
• Mark-up over cost price = $$\frac{2x}{5}$$
• List price = $$\frac{4x}{5} + \frac{2x}{5} = \frac{6x}{5}$$
• Discount = $$\frac{x}{5}$$

Now, please check the following relations:
• Cost price + mark-up = list price
• List price discount = selling price
• Also, profit = selling price – cost price

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Re: A shoe shop owner lists the price of a pair of shoes as the price &nbs [#permalink] 01 Jun 2018, 05:29
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