A shopkeeper offers two successive discounts of 20% each on a sweater and still makes a profit of 60%. By what

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Apr 11, 2021 5:12 pm

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A shopkeeper offers two successive discounts of 20% each on a sweater and still makes a profit of 60%. By what percentage did the shopkeeper mark-up the price of the sweater?

A) 60%

B)100%

C)150%

D)200%

E)250%

OA C

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Sun Apr 11, 2021 5:12 pm

swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: A shopkeeper offers two successive discounts of 20% each on a sweater and still makes a profit of 60%. By what

by swerve » Tue Apr 13, 2021 11:12 am

BTGmoderatorDC wrote: ↑
Sun Apr 11, 2021 5:12 pm
A shopkeeper offers two successive discounts of 20% each on a sweater and still makes a profit of 60%. By what percentage did the shopkeeper mark-up the price of the sweater?

A) 60%

B)100%

C)150%

D)200%

E)250%

OA C

Source: e-GMAT

Let the cost price be 100.
1) First profit of $60\%= 160$
2) This is $(100-20)\%$ of $(100-20)\%$ of marked price or $m$
So $160=0.8\cdot 0.8 \cdot m \Longrightarrow 0.8m=200 \Longrightarrow m=250$

So $m$ is $250-100=150$ over $100$
As a $\%,$ $m$ is $\dfrac{150}{100}\cdot 100=150\%$

Therefore, C

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8175; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A shopkeeper offers two successive discounts of 20% each on a sweater and still makes a profit of 60%. By what

by Scott@TargetTestPrep » Mon Apr 26, 2021 6:44 am

BTGmoderatorDC wrote: ↑
Sun Apr 11, 2021 5:12 pm
A shopkeeper offers two successive discounts of 20% each on a sweater and still makes a profit of 60%. By what percentage did the shopkeeper mark-up the price of the sweater?

A) 60%

B)100%

C)150%

D)200%

E)250%

OA C

Solution:

We can let p be the mark-up price of the sweater, c be the cost of the sweater and create the equation:

p * 0.8 * 0.8 = c + 0.6c

0.64p = 1.6c

p = 1.6c/0.64 = 160c/64 = 10c/4 = 5c/2

That is the mark-up price of the sweater is 2.5 times or 250% the cost of the sweater. Therefore, the price has been marked up by 150%.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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