The price of a book is first decreased by 25% and then increased by 20%. What is the net percentage change in the price of the book compared to the original price?

Introduction / Context:
This question explores successive percentage changes, which occur often in discount and price adjustment problems. A price is first reduced by a certain percentage and then increased by another percentage. The goal is to find the net effect relative to the original price. This requires understanding that percentage changes operate multiplicatively, not additively. Here, a 25% decrease followed by a 20% increase does not bring the price back to the original level, and we must compute the final effective percentage change.

Given Data / Assumptions:
- Initial price of the book is assumed to be some value, say Rs. 100, for convenience.- First, the price decreases by 25%.- Then, the new price is increased by 20%.- We must determine the net percentage change with respect to the original price.- The options are given as numerical values representing the magnitude of the percentage change.

Concept / Approach:
Successive percentage changes are handled by applying each percentage operation step by step and using multiplication factors. A 25% decrease corresponds to multiplying by (1 - 0.25) = 0.75. A 20% increase corresponds to multiplying by (1 + 0.20) = 1.20. The final price is obtained by multiplying the original price by these two factors in sequence. The net percentage change is found by comparing the final price with the original price and converting the difference to a percentage of the original price.

Step-by-Step Solution:
Step 1: Assume the original price of the book is Rs. 100 (this makes percentage calculations easy and does not affect the final percentage change).Step 2: Apply a 25% decrease.New price after decrease = 100 * (1 - 0.25) = 100 * 0.75 = Rs. 75.Step 3: Now apply a 20% increase to the new price.New price after increase = 75 * (1 + 0.20) = 75 * 1.20 = Rs. 90.Step 4: Compare final price with original price.Original price = Rs. 100, final price = Rs. 90.Step 5: Difference = 100 - 90 = Rs. 10.Step 6: Net percentage change = (Difference / Original price) * 100%.Net percentage change = (10 / 100) * 100% = 10%.Step 7: Since final price is lower than the original, this is a 10% decrease.

Verification / Alternative check:
Instead of assuming Rs. 100, use multiplication factors directly.Overall multiplication factor = 0.75 * 1.20 = 0.90.This means the final price is 90% of the original.Therefore, there is a net 10% decrease from the original price.This confirms the earlier calculation using the assumed price of Rs. 100.

Why Other Options Are Wrong:
- 20: This would suggest a 20% net change which is not supported by the product of the factors 0.75 and 1.20.- 30: Incorrectly assumes additive combination of 25% and 5% or some miscalculation of the difference.- 40: Perhaps due to incorrectly adding 25% and 20%, not realizing that successive percentage changes are not additive.

Common Pitfalls:
- Simply adding -25% and +20% to claim a -5% change instead of computing multiplicative effects.- Applying the 20% increase to the original price instead of to the reduced price.- Forgetting that the base for the second percentage is already changed by the first operation.- Not indicating clearly that the net change is a decrease, even though the magnitude is 10%.

Final Answer:
The price undergoes a net 10% decrease compared to the original price.