An article when sold at a gain of 5% yields Rs. 20 more than when sold at a…
2025
An article when sold at a gain of 5% yields Rs. 20 more than when sold at a loss of 5%. The cost price of the article is:
Answer: A. Rs. 200 — When the same article is sold once at a gain of g% and once at a loss of l% on the same cost price, the difference between the two selling prices always…
- A.
Rs. 200
- B.
Rs. 150
- C.
Rs. 100
- D.
Rs. 250
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Correct answer: A
When the same article is sold once at a gain of g% and once at a loss of l% on the same cost price, the difference between the two selling prices always equals (g + l)% of the cost price. This follows directly from Selling Price = Cost Price × (1 ± percentage/100).
Let the cost price of the article be Rs. x.
Selling price at a 5% gain = x + 5% of x = 1.05x.
Selling price at a 5% loss = x − 5% of x = 0.95x.
Difference between the two selling prices = 1.05x − 0.95x = 0.10x.
This difference is given as Rs. 20, so 0.10x = 20, which gives x = 200.
Substituting x = 200 back: selling price at 5% gain = Rs. 210, selling price at 5% loss = Rs. 190, and their difference is Rs. 210 − Rs. 190 = Rs. 20, confirming the cost price is Rs. 200.