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 can do 1/3 of work in 5 days. B can do 2/3 of work in 10 days. In how many days can they complete the entire work together?
A6 days
B7.5 days
C9 days
D10 days
Correct Answer: C. 9 days
Explanation:
A does 1/3 work in 5 days, so full work in 15 days. B does 2/3 work in 10 days, so full work in 15 days. Combined rate = 1/15 + 1/15 = 2/15. Time = 15/2 = 7.5 days. Wait, let me recalculate B: If 2/3 in 10 days, then 1 in 15 days. So both take 15 days individually. Together: 2/15 per day, so 15/2 = 7.5 days.
