A tank full of petrol in Veeru car lasts for 20 days at his usual daily usage. If he starts using 25 percent more petrol every day, for how many days will the same tank full of petrol last?

Introduction / Context:
This question tests your understanding of inverse proportionality in basic quantitative aptitude. When the total quantity of a resource remains constant, such as a full petrol tank, and the rate of consumption increases, the number of days that resource lasts decreases. The relationship between consumption per day and number of days is inversely proportional, which means that if one increases by a certain factor, the other decreases by that same factor. Recognising and applying this idea enables you to solve many time and work or time and consumption problems quickly in competitive exams.

Given Data / Assumptions:
- A full tank of petrol lasts for 20 days at the original daily consumption. - Daily consumption is then increased by 25 percent. - The total quantity of petrol in the tank remains the same. - We assume consumption is steady each day before and after the change.

Concept / Approach:
Let the original daily consumption be C units of petrol per day. If the full tank lasts for 20 days, the total petrol in the tank is Total = 20 * C. When Veeru starts using 25 percent more petrol each day, the new daily consumption becomes C_new = C + 0.25 * C = 1.25 * C. Because the total petrol in the tank is unchanged, the new number of days N_new is given by Total divided by C_new. This is a classic example of inverse proportion: number of days is proportional to 1 divided by daily consumption.

Step-by-Step Solution:
Step 1: Let original daily consumption be C units per day. Step 2: Full tank lasts 20 days, so total petrol in tank = 20 * C. Step 3: New daily consumption after a 25 percent increase = C_new = 1.25 * C. Step 4: New number of days N_new = Total / C_new = (20 * C) / (1.25 * C). Step 5: Simplify N_new: (20 * C) / (1.25 * C) = 20 / 1.25. Step 6: Compute 20 / 1.25. Note that 1.25 = 5 / 4. So 20 / (5 / 4) = 20 * (4 / 5) = 80 / 5 = 16. Step 7: Therefore, the same tank full of petrol will now last 16 days.

Verification / Alternative check:
Another way to think about this is to use the inverse proportion rule directly. If daily consumption increases by 25 percent, it is multiplied by 1.25. To keep the total quantity constant, the number of days must be divided by 1.25. Original days = 20. New days = 20 / 1.25, which we already calculated as 16. You could also view it as follows: 25 percent more usage means Veeru now uses the original amount for 4 days in only 3 days, because 1.25 * 3 = 3.75 which is close to 4 in ratio reasoning. Over 20 days, that reduces to 15 days plus one extra day from the remaining fraction, again giving 16 days when done precisely.

Why Other Options Are Wrong:
18 days: This would correspond to a smaller increase in consumption than 25 percent, so it does not match the given data. 12 days: This implies too large an increase in daily usage; if consumption doubled, the days would halve to 10, not 12. 14 days: This also does not follow from the 20 to 1.25 ratio when calculated correctly.

Common Pitfalls:
A common mistake is to reduce the number of days by 25 percent directly, giving 15 days. This is incorrect because the 25 percent change applies to daily consumption, not directly to the duration. Another error is to treat the relationship as linear rather than inverse, adding or subtracting numbers without considering the multiplication factor. To avoid such mistakes, always remember that when a fixed quantity is consumed faster, time and rate are inversely proportional: days_new = days_old * (old_rate / new_rate). In this problem that means 20 * (1 / 1.25) = 16 days.

Final Answer:
The correct answer is 16 days, because increasing daily petrol usage by 25 percent shortens the duration from 20 days to 20 / 1.25, which equals 16 days.