UPSC Prelims 2001 Q142: Science & Technology – Quantitative Aptitude
Water is filled in a container in such a manner that its volume doubles after every five
minutes. If it takes 30 minutes for the container to be full, in how much time will it be one - fourth
full?
- (a) 7 minutes and 30 seconds
- (b) 10 minutes
- (c) 20 minutes
- (d) 25 minutes
Answer: (c) 20 minutes
Explanation
When the container is one-fourth full
| Time | Fraction full |
|---|---|
| 30 minutes | Full (1) |
| 25 minutes | 1/2 (volume doubles every 5 minutes) |
| 20 minutes | 1/4 |
| 15 minutes | 1/8 |
Given: the water volume doubles every five minutes and the container is full at 30 minutes. Working backwards, it was half full 5 minutes earlier (25 minutes) and one-fourth full another 5 minutes earlier, at 20 minutes.
Answer: (c) 20 minutes.
Why each option is right or wrong
- (a) Incorrect. 7.5 minutes treats the filling as steady, not doubling.
- (b) Incorrect. At 10 minutes the container is only 1/16 full.
- (c) CORRECT. Two halvings back from 30 minutes give 20 minutes.
- (d) Incorrect. At 25 minutes the container is half full.
Key point
Doubling problems: work backwards by halving.
Remember
Doubles every 5 min, full at 30 → quarter full at 20.
Common mistakes
- Taking one-fourth of 30 minutes (7.5) as if filling were steady.
- Stopping at the half-full time (25 minutes).
- Counting halvings forward from zero.
Exam tip
For doubling, count back: full → half → quarter.
Sources
- NCERT Class VIII — Mathematics, chapter 'Exponents and Powers'
- R. S. Aggarwal — Quantitative Aptitude, chapter 'Problems on Numbers'