If an article is sold for ₹ 2220, the percentage of profit earned by the…
2023
If an article is sold for ₹ 2220, the percentage of profit earned by the shopkeeper is the same as the percentage of loss incurred on that article if it is sold for ₹ 1580. At what price should the article be sold to make a profit of 25%?
Answer: C. ₹ 2375 — ConceptWhen the profit percentage at one selling price equals the loss percentage at another selling price, both percentages are calculated on the same cost…
- A.
₹ 2175
- B.
₹ 2275
- C.
₹ 2375
- D.
₹ 2300
Show answer & explanation
Correct answer: C
Concept
When the profit percentage at one selling price equals the loss percentage at another selling price, both percentages are calculated on the same cost price.
Therefore, the cost price is the arithmetic mean of the two selling prices: CP = (higher SP + lower SP) ÷ 2. A 25% profit selling price is 1.25 × CP.
Application
Let the cost price be CP and the common profit/loss amount be d. Then CP + d = ₹2220 and CP − d = ₹1580.
Add the equations: 2CP = ₹2220 + ₹1580 = ₹3800, so CP = ₹1900.
For a 25% profit, selling price = ₹1900 × 1.25 = ₹2375.
Cross-check
The deviations from ₹1900 are equal: ₹2220 − ₹1900 = ₹320 and ₹1900 − ₹1580 = ₹320. Thus the profit and loss percentages are equal, and the required selling price is ₹2375.