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1.  

Directions (Q 39–42): Towns P and Q are 480 km apart on a straight highway. A bus leaves P for Q at 7:00 am at 60 km/h. A car leaves Q for P at 8:00 am at 80 km/h. A truck leaves P for Q at 8:00 am at 40 km/h.

At what time do the bus and the car meet?

Correct Answer: E [11:00 am]

Explanation:

At 8:00 the bus is 60 km out; gap 420 km at 140 km/h → 3 h → 11:00 am.

2.  
(Use the directions above – Time, Speed & Distance, Trains, Boats & Streams, Q 39–42)
When the bus meets the car, how far behind the bus is the truck?

Correct Answer: C [120 km]

Explanation:

Bus: 60 × 4 = 240 km from P; truck: 40 × 3 = 120 km → 120 km behind.

3.  
(Use the directions above – Time, Speed & Distance, Trains, Boats & Streams, Q 39–42)
How far from P does the car meet the truck?

Correct Answer: D [160 km]

Explanation:

At 8:00 gap 480 km, closing at 120 km/h → 4 h; truck 40 × 4 = 160 km from P.

4.  
(Use the directions above – Time, Speed & Distance, Trains, Boats & Streams, Q 39–42)
How many minutes after meeting the bus does the car meet the truck?

Correct Answer: B [60 minutes]

Explanation:

Car meets bus at 11:00 am and the truck at 12:00 noon → 60 minutes.

5.  
Two runners start together from the same point on an 800 m circular track and run in opposite directions at 5 m/s and 3 m/s. After how many seconds do they meet for the first time?

Correct Answer: A [100 s]

Explanation:

Opposite → relative 8 m/s → 800 ÷ 8 = 100 s.

6.  
Two runners start together from the same point on an 800 m circular track and run at 5 m/s and 3 m/s in opposite directions. At how many distinct points on the track do they meet?

Correct Answer: B [8]

Explanation:

Opposite directions: distinct meeting points = 5 + 3 = 8.

7.  
Quantity I: Speed in still water (km/h) of a boat that goes 30 km downstream in 2 hours and 30 km upstream in 3 hours.
Quantity II: Average speed (km/h) of the same boat for that whole round trip.

Correct Answer: A [Quantity I > Quantity II]

Explanation:

I: (15 + 10)/2 = 12.5. II: 60 km ÷ 5 h = 12.

8.  
What is the speed of the stream?
I. The boat goes 24 km downstream in 2 hours.
II. The boat goes 24 km upstream in 3 hours.

Correct Answer: D [Both statements together are needed]

Explanation:

Need both: D = 12, U = 8 → v = (12 − 8)/2 = 2 km/h.

9.  
What is the length of the train?
I. Running at 72 km/h, it crosses a 200 m platform in 18 seconds.
II. Running at 72 km/h, it passes a pole in 8 seconds.

Correct Answer: C [Either statement alone is sufficient]

Explanation:

I: 20 × 18 − 200 = 160 m. II: 20 × 8 = 160 m.

10.  
A train overtakes two people walking in its direction at 3 km/h and 6 km/h in 9 seconds and 10 seconds respectively. The length of the train is:

Correct Answer: A [75 m]

Explanation:

9(v − 5/6) = 10(v − 5/3) → v = 55/6 m/s (33 km/h); L = 9 × (55/6 − 5/6) = 75 m.

11.  
A boat takes 8 hours to go 48 km downstream and 40 km upstream, and 5 hours to go 32 km downstream and 24 km upstream. The speed of the boat in still water is:

Correct Answer: E [12 km/h]

Explanation:

Solve 48/D + 40/U = 8 and 32/D + 24/U = 5 → D = 16, U = 8 → u = 12 km/h.

12.  
Three runners start together from the start line of a 720 m circular track and run in the same direction at 6 m/s, 8 m/s and 9 m/s. After how many seconds are all three at the start line together for the first time?

Correct Answer: D [720 s]

Explanation:

Lap times 120 s, 90 s and 80 s → LCM = 720 s.

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