In aptitude (time and money simplification), Mr. Ankit is on tour to Siachen with a total budget of ₹360. If he extends his tour by 4 days, he must reduce his daily expenditure by ₹3 to stay within the same total amount. For how many days was Mr. Ankit originally on tour?

Introduction / Context:
This is a classic time and money problem that translates directly into a linear equation. Such questions are common in aptitude exams to check whether candidates can convert a word problem into algebraic expressions. The key idea is that the total expense remains fixed while the number of days and daily expenditure change in a related way. Understanding this trade-off is crucial for solving the equation correctly.

Given Data / Assumptions:
- Total amount for the tour: ₹360.
- Let the original number of days be n.
- Original daily expenditure is 360 / n rupees per day.
- If he extends the tour by 4 days, the new number of days is n + 4.
- In that case, he must reduce his daily expenditure by ₹3.
- Total expenditure remains ₹360 in both scenarios.

Concept / Approach:
The concept is to express both daily expenditures in terms of n and equate them according to the given relationship. The original daily expenditure is 360 / n. The new daily expenditure after extending the tour is 360 / (n + 4), and this is ₹3 less than the original daily expenditure. This gives us a single equation in one variable n, which we can solve using algebraic manipulation and factorisation.

Step-by-Step Solution:
Step 1: Let n be the original number of days.Step 2: Original daily expenditure = 360 / n.Step 3: New daily expenditure after extension by 4 days = 360 / (n + 4).Step 4: Given condition: new daily expenditure = original daily expenditure - 3.Step 5: Therefore, 360 / (n + 4) = 360 / n - 3.Step 6: Rearrange the equation: 360 / (n + 4) = (360 - 3n) / n.Step 7: Cross multiply: 360n = (n + 4)(360 - 3n).Step 8: Expand the right-hand side: (n + 4)(360 - 3n) = n * 360 - 3n^2 + 4 * 360 - 12n = 360n - 3n^2 + 1440 - 12n.Step 9: So 360n = 360n - 3n^2 + 1440 - 12n.Step 10: Subtract 360n from both sides: 0 = -3n^2 + 1440 - 12n.Step 11: Rearrange into standard quadratic form: 3n^2 + 12n - 1440 = 0 (multiplying by -1).Step 12: Divide by 3: n^2 + 4n - 480 = 0.Step 13: Factorise: n^2 + 4n - 480 = (n - 20)(n + 24) = 0.Step 14: Solutions are n = 20 or n = -24. Negative days are not meaningful, so n = 20.

Verification / Alternative check:
Check with n = 20: Original daily expenditure = 360 / 20 = 18 rupees per day. If he extends by 4 days, new days = 24. New daily expenditure = 360 / 24 = 15 rupees per day. The decrease in daily expenditure is 18 - 15 = 3 rupees per day, which matches the given condition. Therefore, n = 20 is correct.

Why Other Options Are Wrong:
- 18, 22, 24, 26: For each of these values, the difference between original and new daily expenditure will not be exactly ₹3 when you compute 360 / n and 360 / (n + 4). They do not satisfy the given condition in the problem statement.

Common Pitfalls:
Some students incorrectly assume the daily expenditure remains the same when the number of days changes, which contradicts the problem. Others make algebraic errors when cross multiplying or expanding the brackets. Forgetting to discard the negative root when solving the quadratic equation can also lead to confusion. Always check that the final solution makes practical sense (number of days must be positive).

Final Answer:
Mr. Ankit was originally on tour for 20 days.