Quantitative Aptitude

Problems on Trains

989 Questions
All Passing a moving person or another train 430 Crossing a platform or bridge 379 Crossing a pole or stationary person 104 Meeting point and post-meeting times 52 Journey time, reduced speed, and schedule conditions 24

Problems on Trains Questions

Multiple choice

A train $75$ m long overtook a person who was walking at the rate of $6$ km/hr and passes him in $\displaystyle 7\frac{1}{2}$ seconds. Subsequently it overtook a second person and passed him in $\displaystyle 6\frac{3}{4}$ seconds. At what rate was the second person travelling?
  1. $4$ km/hr
  2. $1$ km/hr
  3. $2$ km/hr
  4. $5$ km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train speed v, person speed u. Relative speed = 75 / (15/2) = 10 m/s = 36 km/hr. v - 6 = 36, so v = 42 km/hr. Second person time = 27/4 seconds. Relative speed = 75 / (27/4) = 300/27 = 100/9 m/s = (100/9) * 3.6 = 40 km/hr. v - u2 = 40. 42 - u2 = 40, so u2 = 2 km/hr.

Multiple choice

Two men are running in the same direction with a speed of $6$ km/hr and $\displaystyle 7\frac{1}{2}$ km/hr. A train running in the same direction crosses them in $5$ sec and $\displaystyle 5\frac{1}{2}$ sec respectively. The length and the speed of the train are
  1. $22.92$ m (approx ) and $22$ km/hr
  2. $22$ m (approx) and $22.5$ km/hr
  3. $22.90$ m(approx) and $20.5$ km/hr
  4. $22.92$ m (approx) and $22.5$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let L be length and V be speed. Convert speeds to m/s: 6 km/h = 5/3 m/s, 7.5 km/h = 25/12 m/s. Relative speeds are (V - 5/3) and (V - 25/12). Using L = (V - v) * t, we get two equations for L and V. Solving yields V = 22.5 km/h and L approx 22.92 m.

Multiple choice

A train travelling at $36$ km/hr passes in $12$ seconds another train half its length travelling in the opposite direction at $54$ km/hr, If it also passes a railway platform in $\displaystyle 1\frac{1}{2}$ minutes what is the length of the platform?
  1. $800$ m
  2. $700$ m
  3. $900$ m
  4. $1000$ m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train 1 speed = 10 m/s, Train 2 speed = 15 m/s. Relative speed = 25 m/s. Length L1 + L2 = 25 * 12 = 300. Since L2 = L1/2, 1.5*L1 = 300, so L1 = 200 and L2 = 100. Passing platform in 90s: (L1 + L_platform) = 10 * 90 = 900. L_platform = 900 - 200 = 700.

Multiple choice

Two train are $2$ km apart and their lengths are $200$ m and $300$ m. They are approaching towards each other with a speed of $20$ m/s and $30$ m/s respectively. After how much time will they cross each other?
  1. $50$ seconds
  2. $100$ seconds
  3. $\displaystyle \frac{25}{3}$ seconds
  4. $150$ seconds
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance to cover = 2km + 200m + 300m = 2500m. Relative speed = 20m/s + 30m/s = 50m/s. Time = 2500 / 50 = 50 seconds.

Multiple choice

Two trains of equal lengths are running on parallel lines in the same direction at the rate of $46$ km/hr and $36$ km/hr. The faster train passes the slower train in $36$ seconds. What is the length of the trains ?
  1. $50$ m
  2. $72$ m
  3. $80$ m
  4. $82$ m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 m/s = 25/9 m/s. Distance covered in 36 seconds = (25/9) * 36 = 100 meters. Since this distance represents the sum of the lengths of two equal trains, each train is 50 meters long.

Multiple choice

A train $X$ starts from New Delhi at $4$ pm and reaches Ghaziabad at $5$ pm. While another train $Y$ starts from Ghaziabad at $4$ pm and reaches New Delhi at $5 : 30$ pm. At what time will the two trains cross each other?
  1. $4 : 30$ pm
  2. $4 : 24$ pm
  3. $4 : 36$ pm
  4. $4 : 41$ pm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train X speed is 1 unit/hour (distance/1 hr). Train Y speed is 1 unit/1.5 hours = 2/3 units/hour. Relative speed is 1 + 2/3 = 5/3 units/hour. They meet at time t = distance / relative speed = 1 / (5/3) = 3/5 hours. 3/5 hours = 36 minutes. Starting at 4 pm, they cross at 4:36 pm.

Multiple choice

A train $108$ m long moving at a speed of $50$ km/hr crosses a train $112$ m long coming from the opposite direction in $6$ seconds. What is the speed of the second train ?
  1. $78$ km/hr
  2. $82$ km/hr
  3. $84$ km/hr
  4. $90$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 108 + 112 = 220 m. Time = 6 s. Relative speed = 220/6 m/s = 110/3 m/s. Convert to km/hr: (110/3) * (18/5) = 132 km/hr. Since they are moving in opposite directions, relative speed = v1 + v2. 132 = 50 + v2, so v2 = 82 km/hr.

Multiple choice

A train overtakes two persons walking along a railway track. The first one walks at $4.5$ km/hr. The other one walks at $5.4$ km/hr. The train needs $8.4$ and $8.5$ seconds, respectively, to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
  1. $81$ km/hr
  2. $82$ km/hr
  3. $83$ km/hr
  4. $84$ km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let train speed be v (km/hr). Relative speeds are (v - 4.5) and (v - 5.4). Convert to m/s: (v - 4.5) * 5/18 and (v - 5.4) * 5/18. Distance = speed * time. Train length L = (v - 4.5) * (5/18) * 8.4 = (v - 5.4) * (5/18) * 8.5. (v - 4.5) * 8.4 = (v - 5.4) * 8.5. 8.4v - 37.8 = 8.5v - 45.9. 0.1v = 8.1. v = 81 km/hr.

Multiple choice

A man sitting in a train travelling at the rate of $50$ km/hr observes that it takes $9$ sec for a goods train travelling in the opposite direction to pass him. If the goods train is $187.5$ m long, find its speed?
  1. $21$ km/hr
  2. $23$ km/hr
  3. $25$ km/hr
  4. $27$ km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = Distance / Time = 187.5 m / 9 s = 20.833 m/s. Convert to km/h: 20.833 * (18/5) = 75 km/h. Since they are moving in opposite directions, relative speed = V_train + V_goods. 75 = 50 + V_goods, so V_goods = 25 km/h.

Multiple choice

Two trains can run at a speed of $54$ km/hr and $36$ km/hr on a parallel tracks. When they are running in opposite directions they pass each other in $10$ s, when they move in the same direction a person sitting in the faster train crosses the other train in $30$ s. Find the length of the trains ( faster and slower respectively ).
  1. $100$ m and $150$ m
  2. $150$ m and $100$ m
  3. $150$ m each
  4. $100$ m each
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, convert the speeds to m/s: 54 km/hr is 15 m/s and 36 km/hr is 10 m/s. When moving in opposite directions, their relative speed is 25 m/s, so the sum of their lengths is 25 * 10 = 250 m. When moving in the same direction, the relative speed is 5 m/s, and the passenger in the faster train takes 30 s to cross the slower train, meaning the length of the slower train is 5 * 30 = 150 m, leaving the faster train's length as 100 m.

Multiple choice

A train $M$ leaves Meerut at $5$ $a.m.$ and reaches Delhi at $9$ $a.m.$ Another train $N$ leaves Delhi at $7$ $a.m.$ and reaches Meerut at $10.30$ $a.m.$ At what time does the two trains cross each other?
  1. $7.36$ $a.m.$
  2. $7.56$ $a.m.$
  3. $8$ $a.m.$
  4. $8.26$ $a.m.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train M speed = D/4. Train N speed = D/3.5. M starts at 5, N at 7. By 7 am, M has traveled 2 hours = D/2. Distance between them at 7 am = D/2. Relative speed = D/4 + D/3.5 = (3.5+4)D/14 = 7.5D/14. Time = (D/2) / (7.5D/14) = 7/7.5 = 14/15 hours = 56 minutes. 7 am + 56 min = 7:56 am.