UPSC Prelims 2007 Q145: Science & Technology – Quantitative Aptitude
A and B can complete work together in 5 days. If A works at twice his speed and B at half of
his speed, this work can be finished in 4 days. How many days would it take for A alone to
complete the job?
- (a) 10
- (b) 12
- (c) 15
- (d) 18
Answer: (a) 10
Explanation
Time and work — A alone
Let A's one-day work = a, B's one-day work = b.
| Condition | Equation |
|---|---|
| Together they finish in 5 days | a + b = 1/5 |
| A at double speed, B at half speed finish in 4 days | 2a + b/2 = 1/4 |
Solve:
From the first, b = 1/5 − a.
Put it in the second: 2a + (1/5 − a)/2 = 1/4.
→ 2a + 1/10 − a/2 = 1/4.
→ (3/2)a = 1/4 − 1/10 = 3/20.
→ a = 1/10.
So A alone takes 10 days.
(And b = 1/5 − 1/10 = 1/10 → B also takes 10 days.)
Answer: (a) 10.
Why each option is right or wrong
- (a) CORRECT. a = 1/10 → A alone takes 10 days.
- (b) Incorrect. 12 days does not satisfy both equations.
- (c) Incorrect. 15 days does not satisfy both equations.
- (d) Incorrect. 18 days does not satisfy both equations.
Key point
a + b = 1/5 and 2a + b/2 = 1/4 → a = 1/10 → A alone = 10 days.
Remember
A alone completes the work in 10 days.
Common mistakes
- Halving A's days instead of doubling A's rate — speed affects work per day.
- Mixing up 'days' and 'work per day' in the equations.
- Skipping a check — put a = 1/10, b = 1/10 back: 2/10 + 1/20 = 5/20 = 1/4 ✔.
Exam tip
Work problems: always convert days to per-day work (1/days), then add rates. Option check is also fast here.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Work)
- NCERT Class VIII Mathematics — Direct and Inverse Proportions