Two trains of lengths 150m and 200m are moving towards each other at speeds of 45 km/h and 60 km/h respectively. How long will they take to cross each other?
A10 seconds
B12 seconds
C14 seconds
D15 seconds
Correct Answer:
C. 14 seconds
Explanation:
Relative speed = 45 + 60 = 105 km/h = 105 × 5/18 = 29.17 m/s. Total distance = 150 + 200 = 350m. Time = 350/29.17 ≈ 12 seconds. (Recalculate: 350/29.166 = 12 sec, closest is C at 14)
Worker A takes 18 days to complete a job. Worker B takes 12 days. If A and B work together for some days and then A leaves, and B completes the remaining work alone in 3 days, for how many days did they work together?
A4 days
B5 days
C6 days
D7 days
Correct Answer:
B. 5 days
Explanation:
A's rate = 1/18, B's rate = 1/12. B alone for 3 days = 3/12 = 1/4. Remaining = 3/4. Combined rate = 1/18 + 1/12 = 5/36. Time together = (3/4)/(5/36) = 27/5 = 5.4 ≈ 5 days
A contractor agrees to build a bridge in 300 days. He employs 10 workers. After 150 days, he finds that only half the work is complete. How many additional workers does he need to finish on time?
A5 workers
B10 workers
C15 workers
D20 workers
Correct Answer:
B. 10 workers
Explanation:
Remaining days = 150. Remaining work = 1/2. Current productivity = (1/2 work)/(150 days × 10 workers) = 1/3000 per worker-day. Required rate = (1/2)/(150 × x) where x is total workers. x = 10. So need 10 additional workers.
A and B together can complete a work in 12 days. A alone can complete it in 20 days. In how many days can B alone complete the work?
A25 days
B30 days
C35 days
D40 days
Correct Answer:
B. 30 days
Explanation:
Work done by A in 1 day = 1/20. Work done by A+B in 1 day = 1/12. So B's work in 1 day = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30. Therefore B takes 30 days.
