Question

A shopkeeper sells an item at a 20% discount but still makes a 20% profit. If the cost price is Rs. 100, what is the marked price? 
 

• A. Rs. 120
• B. Rs. 125
• C. Rs. 150
• D. Rs. 160

Hint:

Always connect CP to SP through profit percentage, and SP to MP through discount percentage, then solve step-by-step.

Answer 1

The Correct Option is C

- Step 1: Understanding terms -

 CP = Cost Price, 

SP = Selling Price, 

MP = Marked Price.
 
- Step 2: Finding SP - 

CP = 100, 

profit = 20 %, 

so: \[ SP = CP \times \left(1 + \frac{20}{100}\right) = 100 \times 1.2 = 120 \] 

- Step 3: Relating SP and MP - 

Discount = 20 %, meaning SP is 80% of MP: \[ SP = 0.8 \times MP \]

Substituting $SP = 120$: \[ 120 = 0.8 \times MP \implies MP = \frac{120}{0.8} = 150 \] 

- Step 4: Verification - Discount = $150 - 120 = 30$ which is $20 %$ of MP, 

and profit = $120 - 100 = 20$ which is $20 %$ of CP. 

- Step 5: Conclusion - MP = Rs. 150, matching option (3).