M07-33

Question

A shop bought a pair of sunglasses for $120 and was selling them at a profit which was equal to 25% of the selling price. Later, the shop owner decided to reduce the selling price by 20%. What was the shop's gross profit on the sale?

A. $0
B. $2
C. $4
D. $6
E. $8

Show Answer

Official Answer

E

A. $0
B. $2
C. $4
D. $6
E. $8

Bunuel · Accepted Answer

Official Solution:

A shop bought a pair of sunglasses for $120 and was selling them at a profit which was equal to 25% of the selling price. Later, the shop owner decided to reduce the selling price by 20%. What was the shop's gross profit on the sale?

A. $0
B. $2
C. $4
D. $6
E. $8

Show Answer

Official Answer

E

A. $0
B. $2
C. $4
D. $6
E. $8

Cost price + Profit = Selling price;
 
Cost price + 0.25*Selling price = Selling price;
 
120 + 0.25*Selling price = Selling price;
 
0.75*Selling price = 120;
 
Selling price = $160
 
After the price reduction, the New Selling price would be 0.8*160 = $128. Therefore, the profit would be New Selling price - Cost price = 128 - 120 = $8.

Answer: E

theGisforGorilla · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

ami000 · Answer

I think this is a  high-quality  question and I agree with explanation.

Dip050701 · Answer

Bunuel  The formula for profit is CP- SP = Profit?

Bunuel · Answer

_______________________________
Selling price - Cost price = Profit.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

vn049636 · Answer

I think this is a  high-quality  question and I agree with explanation.

maddscientistt · Answer

Hi  Bunuel

Help me understand where I'm going wrong : )

Given,

C = 120
P = 25/100 * S

then, P = 25/100 * 80/100 * S

on simplifying,

P = 1/5 * S
P = 1/5 * (P + C)
5P = P + 120
4P = 120
P = 30

Bunuel · Answer

Your mistake is in the equation P = 25/100 * 80/100 * S.

Here's why:

The problem states that profit is 25% of the selling price, so the correct equation is P = 25/100 * S. 
 The price reduction happens after the initial selling price is set, meaning you don't apply the 80% factor to the profit percentage itself.

The correct approach is:

Solve for the original selling price:
 
 120 + 0.25S = S → 0.75S = 120 → S = 160  
 
 Apply the 20% discount:
 
 New selling price = 0.8 * 160 = 128  
 
 Compute the profit:
 
 Profit = 128 - 120 = 8

Your approach incorrectly applies the discount to the profit percentage instead of just the selling price.

M07-33

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