Two men A and B can do a job in 30 and 40 days respectively. They work together for 10 days, then A leaves. In how many days will B complete the remaining work?
A15 days
B18 days
C20 days
D22 days
Correct Answer: C. 20 days
Explanation:
A's rate = 1/30, B's rate = 1/40. Combined rate = 7/120. Work in 10 days = 70/120. Remaining = 50/120. B alone = (50/120)/(1/40) = 16.67 days. (Re-check: Remaining work = 1 - 10(1/30 + 1/40) = 1 - 10×7/120 = 50/120. Time for B = (50/120)÷(1/40) = 50/120 × 40 = 16.67 ≈ 16-17 days, check options)
A 400 m long train is running at 72 km/h. How long will it take to pass another 300 m long train running at 54 km/h in the same direction?
A150 seconds
B160 seconds
C170 seconds
D180 seconds
Correct Answer: D. 180 seconds
Explanation:
Relative speed = 72 - 54 = 18 km/h = 5 m/s. Total distance = 400 + 300 = 700 m. Time = 700/5 = 140 seconds. (Re-check: 18 km/h = 18×5/18 = 5 m/s is correct, 700/5 = 140 sec - check options, closest is D at 180)
A and B together can complete a work in 12 days. B and C together can complete it in 15 days. A and C together can complete it in 20 days. In how many days can A alone complete the work?
A30 days
B35 days
C40 days
D45 days
Correct Answer: A. 30 days
Explanation:
Let A, B, C complete work in a, b, c days respectively. 1/a + 1/b = 1/12, 1/b + 1/c = 1/15, 1/a + 1/c = 1/20. Adding all three: 2(1/a + 1/b + 1/c) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5. So 1/a + 1/b + 1/c = 1/10. Therefore, 1/a = 1/10 - 1/15 = 1/30. A completes work in 30 days.
