The entry fee to an exhibition was Rs. 1 per visitor. Later, the entry fee was reduced by 25%, and as a result the total revenue from ticket sales increased by 20%. By what percentage did the number of visitors increase?

Introduction:
This question belongs to the category of percentage change and deals with the relationship between price, quantity, and revenue. It tests the understanding that when price changes and revenue changes by a certain percentage, the quantity sold must adjust accordingly. Here the price is entry fee and quantity is number of visitors.

Given Data / Assumptions:
Original entry fee per visitor = Rs. 1.
Entry fee is reduced by 25%, so new entry fee is less than Rs. 1.
After the fee reduction, total revenue increases by 20%.
We must find the percentage increase in the number of visitors.

Concept / Approach:
Revenue is equal to price multiplied by quantity. Let the original number of visitors be N and original revenue be R. After the price reduction and increase in revenue, the new revenue becomes 1.20 * R, while the new price becomes 75% of the original price. Using the relationship between revenue and price, we can find the new quantity, and then compute the percentage increase in visitor numbers.

Step-by-Step Solution:
Let the original number of visitors be N. Original entry fee per visitor = Rs. 1. Original revenue R = 1 * N = N. The fee is reduced by 25%. New entry fee = 1 - 25% of 1 = 1 - 0.25 = Rs. 0.75. Given that revenue increases by 20%, so new revenue = 1.20 * R = 1.20 * N. Let the new number of visitors be V. New revenue is also equal to new price * new number of visitors, so 0.75 * V = 1.20 * N. Solve for V in terms of N: V = (1.20 * N) / 0.75. Compute 1.20 / 0.75 = 1.60. So V = 1.60 * N. This means the number of visitors increased to 160% of the original number. Percentage increase in visitors = (V - N) / N * 100 = (1.60 * N - N) / N * 100 = 0.60 * 100 = 60%.
Verification / Alternative check:
Take an example with N = 100 original visitors. Original revenue is Rs. 100. After the fee cut, new price is Rs. 0.75 and revenue must be 20% higher, so new revenue should be Rs. 120. To get Rs. 120 at Rs. 0.75 per visitor, the number of visitors must be 120 / 0.75 = 160. This is an increase from 100 to 160 visitors, which is a 60% rise. This matches the algebraic result exactly.

Why Other Options Are Wrong:
An increase of 20% or 40% would not produce a revenue rise of 20% when combined with a 25% drop in price. An 80% or 100% increase in visitors would exaggerate the revenue change well beyond the stated 20%. Only a 60% rise in visitors gives a revenue that is exactly 20% higher with a price that is 25% lower.

Common Pitfalls:
One frequent mistake is to confuse percentage change in price with percentage change in quantity, or to assume that a 25% reduction in price and 20% increase in revenue must mean a 45% increase in visitors by simple addition. Another common error is failing to express everything in terms of variables and directly guessing. Correct reasoning uses the formula revenue = price * quantity for both the original and changed conditions.

Final Answer:
The number of visitors increased by 60%.