UPSC Prelims 2003 Q57: Science & Technology – Logical Reasoning & Puzzles
Four different candles, which can last for 5 hours, 4 hours, 3 hours and 2 hours of burning,
respectively, are lit in a room at the same instant and allowed to burn till such time that the
three candles in the room get extinguished. The cost of burning each one of these candles is 75
paise per hour. The cost involved is:
- (a) Rs. 2.75
- (b) Rs. 3.75
- (c) Rs. 9.75
- (d) Rs. 12.50
Answer: (c) Rs. 9.75
Explanation
Cost of burning four candles
| Candle | Hours burnt before three candles are out |
|---|---|
| 5-hour candle | 4 hours (still burning) |
| 4-hour candle | 4 hours |
| 3-hour candle | 3 hours |
| 2-hour candle | 2 hours |
Three candles are out when the 4-hour candle finishes, so the burning time is 4 + 4 + 3 + 2 = 13 candle-hours; at 75 paise per hour the cost is 13 x 0.75 = Rs 9.75.
Answer: (c) Rs. 9.75.
Why each option is right or wrong
- (a) Incorrect. Rs 2.75 is far below 13 candle-hours at 75 paise.
- (b) Incorrect. Rs 3.75 is only 5 candle-hours.
- (c) CORRECT. 13 x 0.75 = Rs 9.75 in all.
- (d) Incorrect. Rs 12.50 would require burning the 5-hour candle fully.
Key point
Stop at the time when three of the four candles are extinguished: after 4 hours.
Remember
Candle-hours of 4 + 4 + 3 + 2 = 13 hours cost Rs 9.75.
Common mistakes
- Letting the 5-hour candle burn the full five hours.
- Stopping the count at 2 hours instead of 4.
- Counting four candles for 4 hours each.
Exam tip
Total cost equals the sum of burning hours times the hourly rate.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Puzzle Test)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (puzzles on time and rates)