Tour-budget planning: Mr. Arjun has ₹ 360 for his trip. If he extends his tour by 4 days, he must reduce his daily expense by ₹ 3 to stay within budget. For how many days was the original plan?

Introduction / Context: This is a classic unitary-method / algebra blend about fixed total budget and varying duration. Extending the number of days forces a reduction in daily spending so that the total cost remains the same. We form an equation in the number of days and solve it cleanly.

Given Data / Assumptions:

• Total budget B = ₹ 360.
• Original number of days = d; original daily expense e = 360/d.
• Extended trip: d + 4 days; new daily expense e − 3 = 360/(d + 4).
• d is a positive integer.

Concept / Approach: Equate the two expressions for the new daily expense. This yields a rational equation in d that simplifies to a quadratic. Solve for d and choose the positive, meaningful value.

Step-by-Step Solution:

Verification / Alternative check: Original e = 360/20 = ₹ 18/day. New duration 24 days with ₹ 15/day gives total 24*15 = ₹ 360, consistent.

Why Other Options Are Wrong: 40, 60, 15, 24 do not satisfy the budget relation; only d = 20 preserves the total expense under the given change.

Common Pitfalls: Algebra slips when clearing denominators; forgetting that total budget is fixed in both scenarios.

Final Answer: 20