# Problems on Trains Quiz Set 005

### Question 1

Two equally long trains of length 160m cross each other in 8sec. If one train is twice as fast as the other, then what is the speed of the faster train?

A

96 km/h.

B

97 km/h.

C

95 km/h.

D

98 km/h.

Soln.
Ans: a

Let the speeds be v and 2v. The trains cover a distance equal to the sum of their lengths at a relative speed v + 2v = 3v. We can use the speed distance formula: \$3v = {160 + 160}/8\$, which gives v = \${320/{3 × 8}} × (18/5)\$ = 48km/h. So the speed of the faster train is twice = 96km/h.

### Question 2

Two trains start simultaneously. The first train moves from Mumbai to Baroda, whereas the second train moves from Baroda to Mumbai. After they meet at a point in between, they respectively take 81 hours and 64 hours to reach their destinations. What is the ratio of their speeds?

A

\${8/9}\$.

B

\${17/8}\$.

C

\${26/11}\$.

D

\${35/11}\$.

Soln.
Ans: a

If they take \$t_1 and t_2\$ hours respectively to reach their destinations, then the ratio of their speeds is \$√t_2 : √t_1\$. So we get \$√64 : √81\$, which gives 8 : 9, or \${8/9}\$.

### Question 3

Two trains coming from opposite direction and running respectively at 48km/h and 96km/h cross each other in 8sec. What is the length of each train if the two trains are equal?

A

160 m.

B

161 m.

C

159 m.

D

162 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 48 + 96 = 144km/h × (5/18), or 40m/s. We can use the speed distance formula: sum of lengths = 40 × 8 = 320m. Halving this we get the length of one train = 160m.

### Question 4

A train 882 meters long is moving at a speed of 65m/s. How long will it take to cross a man who is running in the opposite direction at a speed of 61m/s?

A

7 sec.

B

8 sec.

C

6 sec.

D

9 sec.

Soln.
Ans: a

The distance to be covered is equal to the length of the train, so s = 882. This distance has to be covered at a net relative speed equal to the sums of the speeds of the man and the train, so v = 65 + 61 = 126. The time will be distance/speed = \$882/126\$ = 7 s.

### Question 5

Two trains are moving in opposite directions on two parallel tracks. How many seconds will they take to cross each other if the sum of their lengths is 216m, and the sum of their speeds is 72m/s.?

A

3 sec.

B

4 sec.

C

2 sec.

D

5 sec.

Soln.
Ans: a

The total distance is equal to the sum of the lengths of the trains, so s = 216. This distance has to be covered at a net relative speed equal to the sums of the speeds of the two trains, so v = 72. The time will be distance/speed = \$216/72\$ = 3 sec. This Blog Post/Article "Problems on Trains Quiz Set 005" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-13