The price of a cycle is first reduced by 25% and then the new price is further reduced by 20%. These two successive reductions together are equivalent to a single reduction of what percentage on the original price?

Introduction / Context:
This problem tests understanding of successive percentage changes. When a price is reduced by one percentage and then reduced again by another percentage, the net effect is not the simple sum of the two percentages. Instead, you must multiply the remaining fractions of the price. This is a very common concept in discount, profit and loss, and percentage chapters in quantitative aptitude.

Given Data / Assumptions:

Initial price of the cycle is taken as some convenient value, say Rs. 100.

First reduction is 25% of the current price.

Second reduction is 20% of the new price after the first reduction.

We are asked to find the single equivalent percentage reduction compared to the original price.

Concept / Approach:
If a quantity is reduced by x%, then the remaining part is (1 − x / 100) times the original. For two successive reductions x% and y%, the final multiplier is (1 − x / 100) * (1 − y / 100). The equivalent single reduction R% is found from final multiplier = 1 − R / 100. In this question, we apply this to 25% and 20% reductions on a starting price of 100 for easy calculation.

Step-by-Step Solution:
Step 1: Assume original price = Rs. 100.Step 2: After a 25% reduction, new price = 100 * (1 − 25 / 100) = 100 * 0.75 = Rs. 75.Step 3: Now reduce this new price by 20%.20% of 75 = 0.20 * 75 = 15.Step 4: Final price after second reduction = 75 − 15 = Rs. 60.Step 5: Compare final price with original price.Original price = 100, final price = 60, so total reduction = 100 − 60 = 40.Step 6: Equivalent single reduction percentage = (40 / 100) * 100 = 40%.

Verification / Alternative check:
Alternatively, use the formula directly: final multiplier = (1 − 25 / 100) * (1 − 20 / 100) = 0.75 * 0.80 = 0.60. Thus 1 − R / 100 = 0.60, so R / 100 = 0.40 and R = 40%. Both methods agree and confirm the answer.

Why Other Options Are Wrong:
45% is found by wrong simple addition of 25% and 20%, which always overestimates the combined reduction.
35% and 32.5% underestimate the combined effect and do not match the calculated final price of 60 out of 100.
42% is a random intermediate guess and does not correspond to multiplying the reduction factors correctly.

Common Pitfalls:
Many candidates simply add percentages, thinking that 25% + 20% = 45% must be the total reduction. This is incorrect because the second reduction applies to a already reduced price. The correct approach is always to convert each change to a multiplier, multiply them together, and then convert the final multiplier into an equivalent single percentage change.

Final Answer:
The two successive reductions are equivalent to a single reduction of 40% on the original price.