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 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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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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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

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