Q1.
A train 150 meters long is running at a speed of 54 km/hr. How much time will it take to cross a pole?
- 10 seconds
- 8 seconds
- 12 seconds
- 15 seconds
Show answer
Answer: A. 10 seconds
Formula: Time = Distance / Speed
Distance = Length of the train = 150 meters
Speed = 54 km/hr
Convert speed to m/s: 54 * (5/18) = 3 * 5 = 15 m/s
Time = 150 meters / 15 m/s = 10 seconds
Q2.
A train 120 meters long passes a platform 180 meters long in 18 seconds. What is the speed of the train in km/hr?
- 60 km/hr
- 54 km/hr
- 72 km/hr
- 48 km/hr
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Answer: A. 60 km/hr
Formula: Speed = Total Distance / Time
Total Distance = Length of train + Length of platform = 120 + 180 = 300 meters
Time = 18 seconds
Speed in m/s = 300 meters / 18 seconds = 50/3 m/s
Convert speed to km/hr: (50/3) * (18/5) = 10 * 6 = 60 km/hr
Q3.
A train 100 meters long running at 50 km/hr crosses another train 120 meters long running at 32 km/hr in the same direction. How much time will it take for the faster train to cross the slower train?
- 44 seconds
- 36 seconds
- 50 seconds
- 60 seconds
Show answer
Answer: A. 44 seconds
Formula: Time = Total Distance / Relative Speed
Total Distance = Length of train 1 + Length of train 2 = 100 + 120 = 220 meters
Relative Speed (same direction) = Speed of faster train - Speed of slower train = 50 - 32 = 18 km/hr
Convert relative speed to m/s: 18 * (5/18) = 5 m/s
Time = 220 meters / 5 m/s = 44 seconds
Q4.
Two trains, one 160 meters long and the other 140 meters long, are running on parallel tracks in opposite directions. Their speeds are 63 km/hr and 45 km/hr respectively. How much time will they take to cross each other?
- 10 seconds
- 60 seconds
- 8 seconds
- 12 seconds
Show answer
Answer: A. 10 seconds
Formula: Time = Total Distance / Relative Speed
Total Distance = Length of train 1 + Length of train 2 = 160 + 140 = 300 meters
Relative Speed (opposite directions) = Speed of train 1 + Speed of train 2 = 63 + 45 = 108 km/hr
Convert relative speed to m/s: 108 * (5/18) = 6 * 5 = 30 m/s
Time = 300 meters / 30 m/s = 10 seconds
Q5.
A train 150 meters long is running at a speed of 63 km/hr. In how much time will it cross a man sitting in another train 200 meters long, which is moving at 27 km/hr in the same direction?
- 15 seconds
- 6 seconds
- 10 seconds
- 12 seconds
Show answer
Answer: A. 15 seconds
Formula: Time = Distance / Relative Speed
When a train crosses a man sitting in another train, the distance covered is the length of the first train.
Distance = Length of the first train = 150 meters
Relative Speed (same direction) = Speed of first train - Speed of second train = 63 - 27 = 36 km/hr
Convert relative speed to m/s: 36 * (5/18) = 2 * 5 = 10 m/s
Time = 150 meters / 10 m/s = 15 seconds
Q6.
A train 180 meters long is running at 50 km/hr. It crosses another train 120 meters long running at 40 km/hr in the opposite direction. What is the time taken for them to cross each other?
- 12 seconds
- 108 seconds
- 10 seconds
- 15 seconds
Show answer
Answer: A. 12 seconds
Formula: Time = Total Distance / Relative Speed
Total Distance = Length of train 1 + Length of train 2 = 180 + 120 = 300 meters
Relative Speed (opposite directions) = Speed of train 1 + Speed of train 2 = 50 + 40 = 90 km/hr
Convert relative speed to m/s: 90 * (5/18) = 5 * 5 = 25 m/s
Time = 300 meters / 25 m/s = 12 seconds
Q7.
A train crosses a platform 100 meters long in 10 seconds and a man standing on the platform in 6 seconds. Find the length of the train and its speed.
- Length 150m, Speed 90 km/hr
- Length 100m, Speed 60 km/hr
- Length 120m, Speed 72 km/hr
- Length 200m, Speed 120 km/hr
Show answer
Answer: A. Length 150m, Speed 90 km/hr
Let L be the length of the train and S be its speed.
When crossing a man, the distance covered is the length of the train:
L = S * 6 (Equation 1)
When crossing a platform, the distance covered is the length of the train + length of the platform:
L + 100 = S * 10 (Equation 2)
From Equation 1, S = L/6.
Substitute S into Equation 2:
L + 100 = (L/6) * 10
L + 100 = 10L/6
L + 100 = 5L/3
Multiply by 3: 3L + 300 = 5L
300 = 5L - 3L
300 = 2L
L = 150 meters
Now find S using L = 150m in Equation 1:
S = 150 / 6 = 25 m/s
Convert speed to km/hr: 25 * (18/5) = 5 * 18 = 90 km/hr
So, Length = 150m, Speed = 90 km/hr
Q8.
A train A, 150 meters long, crosses a platform 250 meters long in 20 seconds. Another train B, 200 meters long, is moving in the opposite direction to train A. If they cross each other in 10 seconds, what is the speed of train B in km/hr?
- 54 km/hr
- 45 km/hr
- 63 km/hr
- 72 km/hr
Show answer
Answer: A. 54 km/hr
Step 1: Find the speed of Train A.
Formula: Speed = Total Distance / Time
Total Distance for Train A to cross platform = Length of Train A + Length of platform = 150 + 250 = 400 meters
Time = 20 seconds
Speed of Train A (S_A) = 400 / 20 = 20 m/s
Step 2: Find the relative speed of Train A and Train B.
Total Distance for Train A and B to cross each other = Length of Train A + Length of Train B = 150 + 200 = 350 meters
Time = 10 seconds
Relative Speed (S_A + S_B, as they are in opposite directions) = 350 / 10 = 35 m/s
Step 3: Find the speed of Train B.
Relative Speed = S_A + S_B
35 m/s = 20 m/s + S_B
S_B = 35 - 20 = 15 m/s
Step 4: Convert the speed of Train B to km/hr.
S_B in km/hr = 15 * (18/5) = 3 * 18 = 54 km/hr
Q9.
Two trains A and B start from stations P and Q respectively and travel towards each other. After meeting, they take 4 hours and 9 hours respectively to reach their destinations Q and P. If train A's speed is 60 km/hr, what is train B's speed?
- 40 km/hr
- 90 km/hr
- 135 km/hr
- 30 km/hr
Show answer
Answer: A. 40 km/hr
Formula for trains meeting and then continuing to their destinations:
Speed A / Speed B = sqrt(Time B / Time A)
Given:
Speed A = 60 km/hr
Time A (after meeting to reach Q) = 4 hours
Time B (after meeting to reach P) = 9 hours
Substitute the values into the formula:
60 / Speed B = sqrt(9 / 4)
60 / Speed B = 3/2
Cross-multiply to find Speed B:
Speed B = 60 * (2/3)
Speed B = 20 * 2
Speed B = 40 km/hr
Q10.
A train crosses a platform 162 meters long in 18 seconds and another platform 120 meters long in 15 seconds. Find the length of the train and its speed in km/hr.
- Length 90m, Speed 50.4 km/hr
- Length 100m, Speed 48 km/hr
- Length 80m, Speed 54 km/hr
- Length 110m, Speed 45 km/hr
Show answer
Answer: A. Length 90m, Speed 50.4 km/hr
Let L be the length of the train and S be its speed (in m/s).
When crossing the first platform:
Distance = L + 162 meters
Time = 18 seconds
So, L + 162 = S * 18 (Equation 1)
When crossing the second platform:
Distance = L + 120 meters
Time = 15 seconds
So, L + 120 = S * 15 (Equation 2)
From Equation 1, S = (L + 162) / 18
From Equation 2, S = (L + 120) / 15
Equating the two expressions for S:
(L + 162) / 18 = (L + 120) / 15
Cross-multiply:
15 * (L + 162) = 18 * (L + 120)
Divide both sides by 3:
5 * (L + 162) = 6 * (L + 120)
5L + 810 = 6L + 720
810 - 720 = 6L - 5L
L = 90 meters
Now substitute L = 90 into Equation 2 to find S:
90 + 120 = S * 15
210 = S * 15
S = 210 / 15 = 14 m/s
Convert speed to km/hr:
Speed = 14 * (18/5) = 252 / 5 = 50.4 km/hr
So, the length of the train is 90m and its speed is 50.4 km/hr.
