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1.
A train passes a man walking at 6 km/h in the same direction in 9 seconds, and another man walking at 6 km/h towards it in 7.5 seconds. The speed of the train is:
Correct Answer: C [66 km/h]
Explanation:
L = 9(v − 5/3) = 7.5(v + 5/3) → 1.5v = 27.5 → v = 55/3 m/s = 66 km/h (length 150 m).
2.
A boat whose speed in still water is 15 km/h goes 40 km downstream and comes back in 6 hours in all. The speed of the stream is:
Correct Answer: B [5 km/h]
Explanation:
40/(15 + v) + 40/(15 − v) = 6 → 1,200 = 6(225 − v²) → v = 5 km/h.
3.
Two trains start at the same time from stations X and Y towards each other. After they meet, the train from X takes 16 hours and the train from Y takes 9 hours to finish the journey. The ratio of the speed of the train from X to that of the train from Y is:
Correct Answer: E [3 : 4]
Explanation:
Root Swap: √9 : √16 = 3 : 4.
4.
A car covers the first one-third of a distance at 30 km/h, the next one-third at 40 km/h and the last one-third at 60 km/h. Its average speed is:
Correct Answer: A [40 km/h]
Explanation:
3 ÷ (1/30 + 1/40 + 1/60) = 3 ÷ (9/120) = 40 km/h.
5.
A 220 m train running at 90 km/h crosses a train coming from the opposite direction at 54 km/h in 12 seconds. The length of the other train is:
Correct Answer: A [260 m]
Explanation:
Relative 144 km/h = 40 m/s; 40 × 12 = 480 m → 480 − 220 = 260 m.
6.
Sundar goes to his office at 30 km/h and returns at 20 km/h. He spends 5 hours on the road in all. The distance to his office is:
Correct Answer: C [60 km]
Explanation:
D/30 + D/20 = 5 → D × 5/60 = 5 → D = 60 km.
7.
A takes 2 hours more than B to cover 60 km. If A doubles his speed, he takes 1 hour less than B. A's speed is:
Correct Answer: B [10 km/h]
Explanation:
60/a − 60/b = 2 and 60/b − 30/a = 1 → adding: 30/a = 3 → a = 10 km/h (B = 15 km/h).
8.
In a 1,000 m race A beats B by 50 m, and in another 1,000 m race B beats C by 100 m. By how many metres would A beat C in a 1,000 m race?
Correct Answer: E [145 m]
Explanation:
When A runs 1,000, B runs 950; C runs 950 × 900/1,000 = 855 → A beats C by 145 m.
9.
A 125 m long train passes a man running at 5 km/h in the same direction in 10 seconds. The speed of the train is:
Correct Answer: D [50 km/h]
Explanation:
Relative speed = 125 ÷ 10 = 12.5 m/s = 45 km/h → train = 45 + 5 = 50 km/h.
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