P can complete a project in 30 days. Q can complete it in 40 days. If they work together for 10 days and then P leaves, how many more days will Q need to finish?
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.
