UPSC Prelims 2001 Q141: Science & Technology – Quantitative Aptitude
A conveyer belt delivers baggage at the rate of 3 tons in 5 minutes, and a second conveyer
belt delivers baggage at the rate of 1 ton in 2 minutes. How much time will it take to get 33 tons
of baggage delivered using both the conveyer belts?
- (a) 25 minutes and 30 seconds
- (b) 30 minutes
- (c) 35 minutes
- (d) 40 minutes and 45 seconds
Answer: (b) 30 minutes
Explanation
Time to deliver 33 tons using both conveyor belts
| Belt | Rate |
|---|---|
| First belt | 3 tons in 5 minutes = 0.6 ton/min |
| Second belt | 1 ton in 2 minutes = 0.5 ton/min |
| Together | 1.1 tons/min |
| Time for 33 tons | 33 ÷ 1.1 = 30 minutes |
Given: one conveyer belt delivers 3 tons of baggage in 5 minutes and a second delivers 1 ton in 2 minutes. Their rates add up to 1.1 tons a minute, so 33 tons take 33 ÷ 1.1 = 30 minutes.
Answer: (b) 30 minutes.
Why each option is right or wrong
- (a) Incorrect. 25.5 minutes would deliver only about 28 tons.
- (b) CORRECT. 1.1 tons/min × 30 min = 33 tons.
- (c) Incorrect. 35 minutes would deliver 38.5 tons.
- (d) Incorrect. 40.75 minutes is far too long.
Key point
For two machines working together, add their rates, not their times.
Remember
0.6 + 0.5 = 1.1 tons/min → 33 tons in 30 minutes.
Common mistakes
- Adding the times (5 + 2) instead of the rates.
- Averaging the two belts' rates instead of adding.
- Not converting each rate to tons per minute.
Exam tip
Convert both to the same unit (tons per minute), then add.
Sources
- NCERT Class VIII — Mathematics, chapter 'Direct and Inverse Proportions'
- R. S. Aggarwal — Quantitative Aptitude, chapter 'Time and Work'