UPSC Prelims 2010 Q112: Science & Technology – Quantitative Aptitude
A man fills a basket with eggs in such a way that the number of eggs added on each
successive day is the same as the number already present in the basket. This way the basket gets
completely filled in 24 days. After how many days was the basket 1⁄4th full?
- (a) 6
- (b) 12
- (c) 17
- (d) 22
Answer: (d) 22
Explanation
A doubling-basket puzzle: when was it a quarter full?
Each day's added eggs equal the current total, meaning the basket's content doubles every day — filling completely on day 24.
| Step | Reasoning |
|---|---|
| Doubling pattern | Content on day n = 2 × content on day (n−1) |
| Full on day 24 | Let full capacity = C |
| One day earlier (day 23) | Content was C/2 (half full) |
| Two days earlier (day 22) | Content was C/4 (quarter full) |
Why counting backward works:
| Point | Detail |
|---|---|
| Doubling each day | Means halving as you go back one day |
| Quarter-full point | Two days before the basket is completely full |
Answer: (d) 22.
Why each option is right or wrong
- (a) Incorrect. Day 6 is far too early in a doubling sequence that reaches full capacity only on day 24.
- (b) Incorrect. Day 12 also doesn't match the correct 'two days before full' calculation.
- (c) Incorrect. Day 17 doesn't align with the exact doubling backward count.
- (d) CORRECT. Since the basket doubles daily, it was quarter full exactly 2 days before being completely full on day 24, i.e., on day 22.
Key point
With daily doubling, the basket was half full one day before completion (day 23) and quarter full two days before (day 22).
Remember
Basket doubles daily, full on day 24: quarter full exactly 2 days earlier, on day 22.
Common mistakes
- Assuming linear (not exponential/doubling) filling, leading to an incorrect proportional day estimate.
- Miscounting how many days back correspond to each halving step.
- Confusing 'quarter full' with a day much earlier in the sequence than the doubling pattern actually implies.
Exam tip
In a daily-doubling fill pattern, go back ONE day for half-full, TWO days for quarter-full, from the completion day.
Sources
- NCERT Class XI Mathematics — Sequences and Series
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Progressions)