The selling price of an article is Rs. 624 and a shopkeeper got a loss of 22%.…
2025
The selling price of an article is Rs. 624 and a shopkeeper got a loss of 22%. If he marks up same article at 30% above the cost price and get a profit of Rs. 84, then find the discount percentage allowed by the shopkeeper?
- A.
7.5%
- B.
5%
- C.
20%
- D.
10%
- E.
15%
Attempted by 2 students.
Show answer & explanation
Correct answer: E
Concept
Cost price, marked price and discount are linked by two ratios. Loss/profit are always measured on the cost price: SP = CP*(1 - loss%) or CP*(1 + profit%). Discount is always measured on the marked price: Selling Price = MP*(1 - discount%), so discount% = (MP - SP)/MP * 100.
Application
Find CP from the loss sale. A selling price of Rs. 624 came with a 22% loss, so 624 = CP*(1 - 0.22) = 0.78*CP, giving CP = 624/0.78 = Rs. 800.
Find the marked price. The article is marked 30% above cost, so MP = 800*(1 + 0.30) = 800*1.30 = Rs. 1040.
Find the actual selling price in the profit case. A profit of Rs. 84 means SP = CP + 84 = 800 + 84 = Rs. 884.
Find the discount. Discount amount = MP - SP = 1040 - 884 = Rs. 156, so discount% = (156/1040)*100 = 15%.
Cross-check
apply 15% discount to MP directly: 1040*(1 - 0.15) = 1040*0.85 = Rs. 884, which equals CP + profit = 800 + 84. Consistent, so 15% is correct.