An article is sold for Rs 950 after allowing a discount of 5 percent on the marked price. What is the marked price of the article?

Introduction / Context:
This is a straightforward discount problem where the selling price after a given percentage discount is known and the marked price needs to be determined. It reinforces the concept that the selling price with discount is a fixed percentage of the marked price and that we can reverse this relationship algebraically.

Given Data / Assumptions:
Selling price after discount = Rs 950. Discount rate = 5 percent. Marked price is unknown. Discount is applied on marked price only.

Concept / Approach:
If discount is 5 percent, then the customer pays 95 percent of the marked price. That means selling price equals marked price multiplied by 0.95. Therefore, marked price equals selling price divided by 0.95. This formula can be applied directly using the given numbers.

Step-by-Step Solution:
Let marked price be M. Selling price S = M * (1 - 5/100) = 0.95M. We are given S = 950. So 0.95M = 950. Therefore M = 950 / 0.95. Compute 950 / 0.95 = 950 * (1 / 0.95). 0.95 is 95/100, so 1 / 0.95 = 100 / 95 = 20 / 19. Thus M = 950 * 20 / 19. 950 / 19 = 50, so M = 50 * 20 = 1000. Hence the marked price is Rs 1000.

Verification / Alternative check:
Check by forward calculation. If marked price is 1000, 5 percent discount equals 5/100 * 1000 = 50. So selling price becomes 1000 - 50 = 950. This exactly matches the given selling price, confirming that the marked price is correct.

Why Other Options Are Wrong:
For a marked price of 960, 5 percent discount would be 48, giving a selling price of 912. For 955, selling price would be about 907.25. For 945, selling price would be 897.75. A marked price of 1050 would lead to selling price 997.5. None of these equal 950. Only 1000 produces the correct discounted selling price.

Common Pitfalls:
A common error is to add 5 percent of 950 instead of viewing 950 as 95 percent of the marked price. Another mistake is to subtract 5 rupees rather than 5 percent. Carefully expressing the relationship S = 0.95M and solving algebraically avoids these misconceptions.

Final Answer:
The marked price of the article is Rs 1000.