Question

A merchant marks his goods 20% above the cost price and allows a discount of 10%. Find his profit percentage.

Hint:

In profit problems with markup and discount: \[ \text{SP} = \text{CP} \times (1+\text{Markup}) \times (1-\text{Discount}) \] Using this shortcut can save time in competitive exams.

Answer 1

Concept: Profit percentage is calculated using \[ \text{Profit %}=\frac{\text{Profit}}{\text{Cost Price}}\times100 \] When a marked price and discount are involved:

• Marked Price (MP) = Cost Price + Markup
• Selling Price (SP) = MP − Discount

Step 1: Assume the cost price. Let the Cost Price (CP) = ₹100.
Step 2: Calculate the Marked Price. The goods are marked \(20%\) above the cost price. \[ \text{MP} = 100 + 20% \text{ of } 100 \] \[ =100+20=₹120 \]
Step 3: Calculate the Selling Price after discount. Discount = \(10%\) on MP. \[ \text{SP} = 120 - 10% \text{ of }120 \] \[ =120-12=₹108 \]
Step 4: Find the profit. \[ \text{Profit} = SP - CP \] \[ =108-100=₹8 \]
Step 5: Calculate the profit percentage. \[ \text{Profit %}=\frac{8}{100}\times100=8% \]
Step 6: Final Answer. \[ \boxed{\text{Profit Percentage} = 8%} \]