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

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

00:00

A

B

C

D

E

## Global Stats

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

by [email protected] » 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%.