Tour-budget linear equation (extend by 4 days, daily spend falls by ₹3): A traveler has a total budget of ₹360 for daily expenses. He extends the tour by 4 days, which reduces his daily spending by ₹3. Find the original planned number of tour days.

Introduction / Context:This problem turns a budget scenario into a linear equation in the number of days. The total spend is fixed, so daily expense equals 360 divided by the number of days. Extending the tour reduces daily spend by a known amount, giving an equation to solve.

Given Data / Assumptions:

• Total budget = ₹360
• Original days = n → daily spend = 360 / n
• Extended days = n + 4 → new daily spend = 360 / (n + 4)
• New daily spend = old daily spend − ₹3

Concept / Approach:Form the equation 360/(n + 4) = 360/n − 3 and solve for n. This is a rational equation leading to a quadratic that factors cleanly.

Step-by-Step Solution:360/(n + 4) = 360/n − 3Multiply by n(n + 4): 360n = (n + 4)(360 − 3n)Expand: 360n = 360n − 3n^2 + 1440 − 12nRearrange: 3n^2 + 12n − 1440 = 0 → n^2 + 4n − 480 = 0Solve: n = [−4 + √(16 + 1920)] / 2 = (−4 + 44)/2 = 20

Verification / Alternative check:Old daily = 360/20 = ₹18; new daily = 360/24 = ₹15; drop is ₹3, which matches.

Why Other Options Are Wrong:15, 16, 18, 24 do not satisfy the exact ₹3 reduction when checked back with 360/n and 360/(n+4).

Common Pitfalls:Sign slips while expanding or canceling 360n prematurely. Keep terms aligned before simplifying.

Final Answer:20