# Problems on Trains

**Exercise:: Problems on Trains-General Questions**

*1. a km/hr = (a x 5/18)m/s*

*2. a m/s =(a x 18/5)km/hr*

3. Time taken by a train of length ** l** metres to pass a pole or stranding man or a signal post is equal to the time taken by the train to cover

**meters.**

*l*4. Time taken by atrain of length ** l** metres to pass a stationary object of length

**metres is the time taken by the train to cover**

*b***metres.**

*(l+b)*5. Suppose two trains or two bodies are moving in the same direction at ** u** m/s and

**m/s, where**

*v***, then their relative speed is**

*u>v***m/s.**

*(u-v)*6. Suppose two trains or two bodies are moving in opposite directions at ** u** m/s and

**m/s, then their relative speed is**

*v***m/s.**

*(u+v)*7. If two trains of length ** a** metres and

**metres are moving in opposite directions at**

*b***m/s and**

*u***m/s, then time taken by the trains to cross each other =**

*v***sec.**

*(a+b)/(u+v)*8. If two trains of length ** a** metres and

**metres are moving in the same direction at**

*b***m/s and**

*u***m/s, then the time taken by the faster train to cross the slower train =**

*v***sec.**

*(a+b)/(u-v)*9. If two trains or bodies start at the same from points ** A** and

**towards each other and after crossing they take**

*B***and**

*a***sec in reaching**

*b***and**

*B***respectively, then**

*A***(A’s speed): (B’s speed) = (√b: √a)**

**1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?**

A. 120 metres

B. 180 metres

C. 324 metres

D. 150 metres

**Answer: Option D**

**Explanation:**

Speed= 60 x 5/18 m/sec = 50/3 m/sec.

Length of the train = (Speed x Time).

Length of the train = 50/3 x 9 m =

**150 m**

**2. A train, 130 m long is running at the speed of 45 km/hr crosses a bridge in 30 seconds. What is the length of the bridge?**

A. 145 metres

B. 245 metres

C. 325 metres

D. 215 metres

**Answer: Option B**

**Explanation:**

The distance travelled by train to cross the bridges is equal to the total length of train and bridge.

Speed = 45 x 5/18 m/sec = 25/2 m/sec.

Time = 30 sec

Total Distance Travelled = (25/2) x 30 = 375 m

Length of the bridge = 375 -130=

**245 m**

**3. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:**

A. 45 km/hr

B. 50 km/hr

C. 54 km/hr

D. 55 km/hr

**Answer: Option B**

Explanation:

Explanation:

When the train and man are in same direction then relative speed will be the difference between their individual speeds.

Relative Speed= 125/10 m/s =12.5 x 18/5 km/hr = 45 km/hr

Now, let the speed of the train = * x* km/h.

So, Relative speed= 45 km/hr =

*-5*

**x**Speed of the train x = 45+5=

**50 km/hr**

**4. A train moving at 50 km/hr crosses a bridge in 45 seconds.The length of train is 150 m. Find the length of bridge :**

A. 445 m

B. 455 m

C. 465 m

D. 475 m

**Answer: Option D**

Explanation:

Explanation:

The distance travelled by train to cross the bridges is equal to the total length of train and bridge.

speed of train= 50 km/h = 50 x 5/18 m/s= 125/9 m/s

Time = 45 sec

Total distance travelled by train to cross the bridge= (125/9)X45 = 625 m

Length of bridge=

**total distance travelled - Length of train**= 625-150=

**475 m**

**5. A train, 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?**

A. 40 sec

B. 42 sec

C. 45 sec

D. 48 sec

**Answer: Option A**

Explanation:

Explanation:

Speed of train= 45 km/h = 45 x 5/18 m/s= 25/2 m/s

Total distance travelled = 360 + 140 = 500 m

Time Taken = Total Distance/ Speed = 500/(25/2) =

**40 sec**

**6. A train of length 110 m is running at a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to the train? **

A. 8 sec

B. 10 sec

C. 6 sec

D. 15 sec

**Answer: Option C**

Explanation:

Explanation:

Distance = 110 m

Relative speed = 60 + 6 = 66 km/hr = 66 x (5/18) = 55/3 m/s

Time taken = Distance/Speed = 110/ (55/3) = **6 sec**

**7. A train 100 m long is running at the speed of 30 km/hr. Find the time taken by train to pass a man standing near the railway line. **

A. 8 sec

B. 12 sec

C. 15 sec

D. 16 sec

**Answer: Option B**

Explanation:

Explanation:

Speed of the train = 30 km/hr = 30 x 5/18 m/s = (25/3) m/s

Distance= Length of train = 100 m

Time taken = Distance/Speed = 100/ (25/3) = **12 sec**

**8. A train 100 m long is moving at a speed of 50 km/hr crosses a train 120 m long coming from opposite direction in 6 seconds. The speed of second train is : **

A. 45 km/h

B. 132 km/h

C. 63 km/h

D. 82 km/h

**Answer: Option D**

Explanation:

Explanation:

Let the Speed of second train =

**x km/h**

Relative speed = (50 +

**x**) km/h

Total Distance covered= (100 m + 120 m) = 220 m = 0.22

**km**

Time = 6 sec = 6/ (60 x 60) hr =

**1/600 hr**

Now, Speed = Distance/ Time

(50 +

**x**) =0.22 / (1/600)

50 +

**x**=132

**x**=

**82 km/h**

Hence, Speed of second train =**x km/h** = **82 km/h**

**9. A train moving with uniform speed crosses a man standing at platform in 2 seconds and a bridge of length 250 m in 7 seconds.The length of train is :**

A. 75 m

B. 85 m

C. 100 m

D. 107 m

**Answer: Option C**

Explanation:

Explanation:

Let the length of train =

**x m**

Speed of train =

**x**/2 = (

**x**+250)/7

7

**x**= 2 (

**x**+ 250)

7

**x**= 2

**x**+ 500

5

**x**= 500

**x = 100 m**

Hence, length of train =

**x m**=

**100 m**

**10. A train 150 m long is running with a speed of 68 km/h. In what time will it pass a man running at 8 km/h in the same direction to the train.**

A. 5 sec

B. 7 sec

C. 9 sec

D. 12 sec

**Answer: Option C**

Explanation:

Explanation:

Relative Speed =

**(68 - 8) km/h = 60 km/h**

Convert speed into m/s = 60 km/h x (5/18) =

**(50/3) m/s**

Time taken by train to cross the man = Distance/ Speed

= 150/ (50/3)

= 150 x 3/50

=

**9 sec**

Hence, Time taken =

**9 sec**