Question:
If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?
If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?
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If SP = CP, then the discount fraction must balance the markup fraction. A discount of 40% (\( 2/5 \)) on MP means SP is \( 3/5 \) of MP. Therefore, MP is \( 5/3 \) of SP (and CP). \( 5/3 = 1 + 2/3 \), so the markup is \( 2/3 \) or 66.66%.
Updated On: May 9, 2026
- 28.57
- 40
- 66.66
- 58.33
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
A merchant applies a 40% discount on his Marked Price (MP) and ends up selling the item exactly at his Cost Price (CP). We need to find by what percentage the Marked Price was raised above the Cost Price (the mark up percentage).
Step 2: Key Formula or Approach:
Selling Price (SP) = Marked Price (MP) - Discount.
Mark up percentage = \( \frac{\text{MP} - \text{CP}}{\text{CP}} \times 100 \).
Step 3: Detailed Explanation:
Let the Cost Price (CP) of the goods be Rs. 100.
The merchant sells the goods exactly at the cost price, so the Selling Price (SP) is also Rs. 100.
He offers a discount of 40% on the Marked Price (MP).
\[ \text{SP} = \text{MP} - (40% \text{ of MP}) \] \[ \text{SP} = \text{MP} \times (1 - 0.40) \] \[ \text{SP} = 0.60 \times \text{MP} \] Substitute the value of SP:
\[ 100 = 0.60 \times \text{MP} \] \[ \text{MP} = \frac{100}{0.60} = \frac{1000}{6} = \frac{500}{3} \approx 166.66 \] The mark up is the difference between MP and CP:
\[ \text{Mark up} = \text{MP} - \text{CP} = 166.66 - 100 = 66.66 \] Since we assumed the CP to be 100, the mark up amount is numerically equal to the mark up percentage.
Step 4: Final Answer:
The % mark up was 66.66%.
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