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A dealer allows a 30% discount on the marked price of an item. What is the marked price of the item if its sale price is ₹12,460?
₹17,800
₹16,760
₹16,800
₹17,860
₹17,800
Since the sale price is after a 30% discount, it represents 70% of the marked price. Divide the sale price by 0.70 to get the marked price directly.
Discount percentage = 30%, Sale price = ₹12,460
Marked Price=1−100Discount%Sale Price
Since the sale price is after a 30% discount, it represents 70% of the marked price. Divide the sale price by 0.70 to get the marked price directly.
Many students mistakenly calculate 30% of the sale price and add it back, instead of taking 70% of the marked price as the sale price.
Step 1: Understand the Relationship
The sale price is obtained after giving a 30% discount on the marked price. Therefore, the sale price represents 100%−30%=70% of the marked price.
Selling Percentage=70%=0.70
Step 2: Set up the Formula
Let the marked price be M. The equation relating marked price, discount, and sale price is:
M×(1−10030)=12,460
Step 3: Solve for Marked Price (M)
Simplify the percentage and solve for M by dividing the sale price by 0.70:
M=0.7012,460=17,800
A is correct because the marked price calculated is ₹17,800.
Profit, loss, and discount problems frequently use percentage bases. Always relate discount to the marked price and profit/loss to the cost price.
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