Question
Which of the following statement(s) is/are correct?
I. The marked price of an article is 50% more than its cost price. The profit earned on selling the article at 20% discount would be 300% more than the profit earned on selling the same article at 30% discount. II. A seller sold an article for Rs. 840, earning a total profit of 40%. If he marked up the price of the article by 50% and sold it after giving a flat discount of Rs. 150, then he would earn the same profit as he had earned earlier. Which of the following statement(s) is/are correct?I. The marked price of an article is 50% more than its cost price. The profit earned on selling the article at 20% discount would be 300% more than the profit earned on selling the same article at 30% discount.II. A seller sold an article for Rs. 840, earning a total profit of 40%. If he marked up the price of the article by 50% and sold it after giving a flat discount of Rs. 150, then he would earn the same profit as he had earned earlier.Solution
For statement I: Let the cost price (CP) of the article be Rs. 100x.
So, marked price (MP) = 100x × 1.5 = 150x.
Selling price when sold at 20% discount = 150x × 0.8 = 120x.
Profit at 20% discount = 120x − 100x = 20x.
Selling price when sold at 30% discount = 150x × 0.7 = 105x.
Profit at 30% discount = 105x − 100x = 5x.
Statement says: profit at 20% discount is 300% more than profit at 30% discount.
“300% more” = original + 300% of original = 400% of original = multiply by 4.
Check: 5x × 4 = 20x.
So 20x = 20x → Statement I is true.
For statement II: Selling price = Rs. 840; profit = 40%.
So CP = 840 ÷ 1.40 = Rs. 600.
Profit earlier = 840 − 600 = Rs. 240.
If he marks up the price by 50%: Marked price = 600 × 1.5 = Rs. 900.
After discount of Rs. 150, selling price = 900 − 150 = Rs. 750.
Profit now = 750 − 600 = Rs. 150.
150 ≠ 240 → Statement II is false.
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