Q1): A car travels 120 km at 40 km/h and another 120 km at 60 km/h. What is the average speed?
A) 45 km/h
B) 48 km/h
C) 50 km/h
D) 52 km/h
Answer: B) 48 km/h
Explanation:
- Step 1: For equal distances: Average speed = (2ab)/(a + b)
- Step 2: a = 40, b = 60 (km/h)
- Step 3: Average = (2×40×60)/(40+60) = 4800/100
- Step 4: Average = 48 km/h
- Final: Option B is correct
Q2): A person travels 3 hours at 30 km/h and 2 hours at 45 km/h. Find the average speed.
A) 33 km/h
B) 36 km/h
C) 37 km/h
D) 39 km/h
Answer: B) 36 km/h
Explanation:
- Step 1: Formula: Average speed = Total distance ÷ Total time
- Step 2: Distance₁ = 30×3 = 90 km, Distance₂ = 45×2 = 90 km
- Step 3: Total distance = 90 + 90 = 180 km
- Step 4: Total time = 3 + 2 = 5 h → Average = 180 ÷ 5 = 36
- Final: Option B is correct
Q3): A train 180 m long runs at 54 km/h. How much time will it take to cross a 270 m platform?
A) 24 s
B) 28 s
C) 30 s
D) 32 s
Answer: C) 30 s
Explanation:
- Step 1: Total distance = Train length + Platform length = 180 + 270 = 450 m
- Step 2: Convert 54 km/h to m/s: 54×(5/18) = 15 m/s
- Step 3: Time = Distance ÷ Speed = 450 ÷ 15
- Step 4: Time = 30 s
- Final: Option C is correct
Q4): Two trains of lengths 150 m and 100 m move in the same direction at 54 km/h and 36 km/h. Time taken to cross each other is:
A) 40 s
B) 45 s
C) 50 s
D) 55 s
Answer: C) 50 s
Explanation:
- Step 1: Total distance to cross = 150 + 100 = 250 m
- Step 2: Speeds in m/s: 54 km/h = 15 m/s, 36 km/h = 10 m/s
- Step 3: Same direction relative speed = 15 − 10 = 5 m/s
- Step 4: Time = 250 ÷ 5 = 50 s
- Final: Option C is correct
Q5): Speed of a boat in still water is 12 km/h and stream speed is 3 km/h. Time taken to travel 30 km upstream is:
A) 3 h
B) 3 h 20 min
C) 3 h 30 min
D) 4 h
Answer: B) 3 h 20 min
Explanation:
- Step 1: Upstream speed = (Still water speed − Stream speed)
- Step 2: Upstream speed = 12 − 3 = 9 km/h
- Step 3: Time = Distance ÷ Speed = 30 ÷ 9 = 10/3 h
- Step 4: 10/3 h = 3 h 20 min
- Final: Option B is correct
Q6): Two cars move towards each other at 45 km/h and 55 km/h. If they are 220 km apart, when will they meet?
A) 2 h
B) 2 h 12 min
C) 2 h 20 min
D) 2 h 30 min
Answer: B) 2 h 12 min
Explanation:
- Step 1: Relative speed (towards each other) = 45 + 55 = 100 km/h
- Step 2: Time = Distance ÷ Relative speed = 220 ÷ 100 = 2.2 h
- Step 3: 0.2 h = 0.2×60 = 12 min
- Final: They meet in 2 h 12 min → Option B
Q7): A starts walking at 4 km/h. B starts from the same point 30 minutes later at 6 km/h in the same direction. After how much time (from B’s start) will B catch A?
A) 30 min
B) 45 min
C) 1 hour
D) 1 h 30 min
Answer: C) 1 hour
Explanation:
- Step 1: A’s head start time = 30 min = 0.5 h
- Step 2: Head start distance = 4×0.5 = 2 km
- Step 3: Relative speed = 6 − 4 = 2 km/h
- Step 4: Catch time = 2 ÷ 2 = 1 h
- Final: Option C is correct
Q8): A circular track is 400 m long. Two runners start together in the same direction at 6 m/s and 4 m/s. Time for the faster to lap the slower is:
A) 150 s
B) 180 s
C) 200 s
D) 240 s
Answer: C) 200 s
Explanation:
- Step 1: To “lap”, faster must gain 1 full round = 400 m
- Step 2: Relative speed = 6 − 4 = 2 m/s
- Step 3: Time = 400 ÷ 2 = 200 s
- Final: Option C is correct
Q9): A train covers a distance in 3 hours at 60 km/h. If its speed becomes 75 km/h, time taken to cover the same distance is:
A) 2 h 15 min
B) 2 h 24 min
C) 2 h 30 min
D) 2 h 40 min
Answer: B) 2 h 24 min
Explanation:
- Step 1: Distance = Speed × Time = 60×3 = 180 km
- Step 2: New time = Distance ÷ New speed = 180 ÷ 75 = 2.4 h
- Step 3: 0.4 h = 0.4×60 = 24 min
- Final: Time = 2 h 24 min → Option B
Q10): A bus takes 30 minutes more to cover 150 km when its speed is reduced by 10 km/h. What was the original speed?
A) 50 km/h
B) 55 km/h
C) 60 km/h
D) 65 km/h
Answer: C) 60 km/h
Explanation:
- Step 1: Let original speed = v km/h, reduced speed = (v − 10) km/h
- Step 2: Time difference: 150/(v−10) − 150/v = 0.5 (hours)
- Step 3: 150v − 150(v−10) = 0.5v(v−10)
- Step 4: 1500 = 0.5(v² − 10v) → 3000 = v² − 10v
- Step 5: v² − 10v − 3000 = 0 → v = 60 (valid)
- Final: Option C is correct
Q11): Convert 18 m/s into km/h.
A) 62.8 km/h
B) 63.8 km/h
C) 64.8 km/h
D) 65.8 km/h
Answer: C) 64.8 km/h
Explanation:
- Step 1: Formula: m/s to km/h = × (18/5)
- Step 2: Speed = 18 m/s
- Step 3: 18×(18/5) = 324/5 = 64.8
- Final: Option C is correct
Q12): A train runs at 54 km/h. It passes a man in 10 seconds and crosses a platform in 25 seconds. Length of the platform is:
A) 200 m
B) 210 m
C) 225 m
D) 240 m
Answer: C) 225 m
Explanation:
- Step 1: Convert speed: 54 km/h = 54×(5/18) = 15 m/s
- Step 2: Train length = 15×10 = 150 m
- Step 3: Total distance (train + platform) = 15×25 = 375 m
- Step 4: Platform length = 375 − 150 = 225 m
- Final: Option C is correct
Q13): A car travels 100 km at 50 km/h, stops for 20 minutes, then travels 50 km at 60 km/h. Average speed for the whole trip is:
A) 45.0 km/h
B) 46.5 km/h
C) 47.4 km/h
D) 48.5 km/h
Answer: C) 47.4 km/h
Explanation:
- Step 1: Time₁ = 100/50 = 2 h
- Step 2: Stop time = 20 min = 1/3 h
- Step 3: Time₂ = 50/60 = 5/6 h
- Step 4: Total time = 2 + 1/3 + 5/6 = 19/6 h
- Step 5: Average speed = Total distance ÷ Total time = 150 ÷ (19/6) = 900/19 ≈ 47.4
- Final: Option C is correct
Q14): Two cities are 360 km apart. If speed is increased by 20%, travel time reduces by 1 hour. Original speed is:
A) 48 km/h
B) 54 km/h
C) 60 km/h
D) 72 km/h
Answer: C) 60 km/h
Explanation:
- Step 1: Let original speed = v, original time = t → Distance = vt = 360
- Step 2: New speed = 1.2v, new time = (t − 1)
- Step 3: Same distance: vt = 1.2v(t − 1)
- Step 4: t = 1.2t − 1.2 → 0.2t = 1.2 → t = 6 h
- Step 5: v = 360 ÷ 6 = 60 km/h
- Final: Option C is correct
Q15): A boat takes 5 hours to travel 30 km upstream and 3 hours to travel 30 km downstream. Speed of the boat in still water is:
A) 6 km/h
B) 7 km/h
C) 8 km/h
D) 9 km/h
Answer: C) 8 km/h
Explanation:
- Step 1: Upstream speed = 30/5 = 6 km/h
- Step 2: Downstream speed = 30/3 = 10 km/h
- Step 3: Still water speed = (Upstream + Downstream)/2 = (6+10)/2
- Step 4: Still water speed = 8 km/h
- Final: Option C is correct
Q16): A person is 12 minutes late if he walks at 5 km/h, and 8 minutes early if he walks at 6 km/h. Distance is:
A) 8 km
B) 9 km
C) 10 km
D) 12 km
Answer: C) 10 km
Explanation:
- Step 1: Total time difference = 12 min + 8 min = 20 min = 1/3 h
- Step 2: Time at 5 km/h − Time at 6 km/h = 1/3
- Step 3: D/5 − D/6 = 1/3
- Step 4: D×(1/30) = 1/3 → D = 10 km
- Final: Option C is correct
Q17): In a 200 m race, A runs at 10 m/s. He gives B a start of 20 m and still wins by 2 seconds. B’s speed is:
A) 7.5 m/s
B) 8.0 m/s
C) 8.18 m/s
D) 8.5 m/s
Answer: C) 8.18 m/s
Explanation:
- Step 1: A’s time = Distance ÷ Speed = 200 ÷ 10 = 20 s
- Step 2: A wins by 2 s, so B’s time = 20 + 2 = 22 s
- Step 3: B runs 180 m (because of 20 m start)
- Step 4: B’s speed = 180 ÷ 22 = 8.1818… m/s
- Final: Approx 8.18 m/s → Option C
Q18): Two trains of lengths 150 m and 200 m move in opposite directions at 36 km/h and 54 km/h. Time to cross each other is:
A) 12 s
B) 14 s
C) 16 s
D) 18 s
Answer: B) 14 s
Explanation:
- Step 1: Total distance = 150 + 200 = 350 m
- Step 2: Convert speeds: 36 km/h = 10 m/s, 54 km/h = 15 m/s
- Step 3: Relative speed (opposite) = 10 + 15 = 25 m/s
- Step 4: Time = 350 ÷ 25 = 14 s
- Final: Option B is correct
Q19): A train runs at 72 km/h and crosses a 120 m platform in 12 seconds. Length of the train is:
A) 100 m
B) 110 m
C) 120 m
D) 130 m
Answer: C) 120 m
Explanation:
- Step 1: Convert 72 km/h to m/s: 72×(5/18) = 20 m/s
- Step 2: Total distance covered in 12 s = 20×12 = 240 m
- Step 3: Total distance = Train length + Platform length
- Step 4: Train length = 240 − 120 = 120 m
- Final: Option C is correct
Q20): A person cycles to office at 15 km/h and returns at 10 km/h. Total travel time is 5 hours. One-way distance is:
A) 24 km
B) 30 km
C) 36 km
D) 40 km
Answer: B) 30 km
Explanation:
- Step 1: Let one-way distance = d km
- Step 2: Total time = d/15 + d/10 = 5
- Step 3: Take LCM 30: (2d + 3d)/30 = 5
- Step 4: 5d/30 = 5 → d/6 = 5 → d = 30
- Final: Option B is correct