If two successive discounts of 25% and 30% are given on the marked price of an item, then what is the ratio of the marked price to the final selling price?

Introduction / Context:
This question concerns successive discounts on a marked price and asks for the ratio of the original marked price to the final selling price. Successive discounts do not add directly as percentages; instead, each discount applies on the reduced price. This is a common profit and loss concept in aptitude exams.

Given Data / Assumptions:

• First discount = 25% on marked price.
• Second discount = 30% on the reduced price.
• We need the ratio Marked Price : Selling Price.
• No taxes or other charges are involved.

Concept / Approach:
We assume a convenient marked price, typically 100 units, to make percentage calculations easy. We then apply the first discount to find the new price and then apply the second discount on that reduced value. The resulting price is the final selling price. Then we express Marked Price : Selling Price as a simplified ratio.

Step-by-Step Solution:

Verification / Alternative check:
We can compute the combined discount factor directly. Price factor after first discount = 0.75. Price factor after second discount = 0.70. Total factor = 0.75 * 0.70 = 0.525. So, SP = 0.525 * MP. Therefore, MP/SP = 1 / 0.525 ≈ 1.9047, which equals 40/21 ≈ 1.9047. This confirms the ratio 40 : 21.

Why Other Options Are Wrong:

• 20 : 7 is approximately 2.857, which would imply a much larger discount than actually given.
• 20 : 17 and 40 : 33 correspond to different combined discount factors and do not match the successive discounts of 25% and 30%.

Common Pitfalls:
One common mistake is to simply add the discounts (25% + 30% = 55%) and treat it as a single discount, which is incorrect because the second discount applies on a reduced price, not the original marked price. Another mistake is to mis-handle decimal calculations when computing 30% of 75. Working carefully or using fractions avoids these problems.

Final Answer:
The ratio of marked price to selling price is 40 : 21.