Difficulty: Easy
Correct Answer: Rs. 900
Explanation:
Introduction / Context:
This problem is another example of reversing a given percentage discount to find the original marked price. Knowing how to move from selling price back to marked price is very important for understanding how discounts affect prices and for solving many commercial math problems.
Given Data / Assumptions:
Concept / Approach:
A discount of 5% means that the customer pays 95% of the marked price. Therefore, SP = 95% of M = 0.95M. The given SP is 855, so we form the equation 0.95M = 855 and solve for M by dividing by 0.95. This is a standard reverse percentage calculation.
Step-by-Step Solution:
Step 1: Let M be the marked price.
Step 2: After a 5% discount, the customer pays 95% of M, so SP = 0.95M.
Step 3: Given that SP = 855, we have 0.95M = 855.
Step 4: Solve for M: M = 855 / 0.95.
Step 5: Compute M = 900.
Step 6: So, the marked price of the item is Rs. 900.
Verification / Alternative check:
Check the result by applying the 5% discount on the marked price of Rs. 900. Discount = 5% of 900 = (5 / 100) * 900 = 45. Selling price = 900 - 45 = 855, which matches the given selling price. This confirms that the marked price of Rs. 900 is correct.
Why Other Options Are Wrong:
Rs. 812.25 and Rs. 897.75: These values do not produce a selling price of 855 when a 5% discount is applied.
Rs. 814: After a 5% discount, the resulting selling price would be lower than 773.3, not 855.
Rs. 950: A 5% discount on 950 gives 902.5, which is not equal to 855.
Common Pitfalls:
Sometimes students attempt to subtract 5 from 855 or divide 855 by 5 directly, both of which do not represent the correct concept. Always remember that a percentage discount is applied to the marked price, and to reverse it, you must divide by the remaining percentage (in decimal form), not by the discount percentage.
Final Answer:
The marked price of the item is Rs. 900.
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