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 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?
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Always connect CP to SP through profit percentage, and SP to MP through discount percentage, then solve step-by-step.
Updated On: Sep 21, 2026
- Rs. 120
- Rs. 125
- Rs. 150
Rs. 160
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The Correct Option is C
Solution and Explanation
- 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).
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