In a hostel, the rent per room is increased by 20% and at the same time the number of rooms is also increased by 20%. If the hostel is always full, what is the percentage change in the total daily collection at the cash counter?

Introduction / Context:
This problem checks understanding of percentage change when two related quantities change at the same time. Here, the total collection in a hostel depends on both the rent per room and the number of rooms occupied. When both factors are changed, we must multiply the corresponding change factors instead of simply adding percentages. This type of question is standard in percentage and profit related topics in aptitude exams.

Given Data / Assumptions:
- Rent per room increases by 20 percent.
- Number of rooms increases by 20 percent.
- The hostel is assumed to be fully occupied both before and after the change.
- We are asked to find the net percentage change in total collection at the cash counter.

Concept / Approach:
Total collection for one day is given by:
Total collection = Number of rooms * Rent per room. When both the rent and the number of rooms increase by certain percentages, we convert each percentage change into a multiplicative factor. An increase of 20% corresponds to a factor of 1.20. The new total collection is obtained by multiplying both factors with the original total. The overall percentage change is then derived from the ratio of new total collection to old total collection.

Step-by-Step Solution:
Let the original number of rooms be R. Let the original rent per room be P. Original total collection = R * P. After a 20% increase in rent, new rent per room = P * 1.20. After a 20% increase in rooms, new number of rooms = R * 1.20. New total collection = (R * 1.20) * (P * 1.20) = R * P * 1.20 * 1.20. So, new total collection = R * P * 1.44. Factor of change = New total / Old total = (R * P * 1.44) / (R * P) = 1.44. Net percentage increase = (1.44 - 1) * 100% = 0.44 * 100% = 44%.

Verification / Alternative check:
We can choose simple numbers to verify. Suppose there were originally 100 rooms at a rent of Rs. 100 each. Then original collection is 100 * 100 = Rs. 10,000. After a 20% increase, rooms become 120 and rent becomes Rs. 120. New collection is 120 * 120 = Rs. 14,400. The increase is 14,400 - 10,000 = Rs. 4,400, which is 44% of 10,000. This confirms that the correct net increase is 44%.

Why Other Options Are Wrong:
30% and 40%: These values might come from simply adding or partially adding the two 20% increases, but adding is not correct when both factors multiply the total.
48%: This could result from an incorrect assumption or arithmetic error when dealing with the factors.
36%: This value does not correspond to the correct multiplicative effect of 1.20 * 1.20.

Common Pitfalls:
Many learners add percentages directly, for example 20% + 20% = 40%, and think the answer is 40%. This is wrong because total collection depends on the product of two quantities, and both are changing. When two changes occur simultaneously and independently, we must convert each change into a factor and then multiply those factors. Forgetting this rule leads to wrong answers in many percentage change problems.

Final Answer:
The total collection at the hostel cash counter increases by 44 percent.