# Problems on Trains Quiz Set 004

### Question 1

A train of length 73m is running at a speed of 57m/s. How long will it take to cross a tunnel of length 41m?

A

2 sec.

B

3 sec.

C

5 sec.

D

4 sec.

Soln.
Ans: a

The total distance to be covered is equal to the length of the train plus the length of the tunnel. By the time and distance formula, we get time = distance/speed, which gives \${73 + 41}/57\$ = 2s.

### Question 2

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.

### Question 3

A train is moving at a speed of 60m/s. It takes 5 seconds to cross a jeep that is travelling in the opposite direction at a speed of 76m/s. What is the length of the train?

A

680 meters.

B

681 meters.

C

679 meters.

D

682 meters.

Soln.
Ans: a

The distance to be covered is equal to the length of the train. This distance has to be covered at a net relative speed equal to the sums of the speeds of the jeep and the train, so v = 60 + 76 = 136. The length of the train will be time × speed = \$5 × 136\$ = 680meters.

### Question 4

Two trains start simultaneously. The first train moves from A to B, whereas the second train moves from B to A. After they meet at a point in between, they respectively take 25 hours and 64 hours to reach their destinations. What is the ratio of their speeds?

A

\${8/5}\$.

B

\${13/4}\$.

C

\${3/7}\$.

D

\${23/7}\$.

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 : √25\$, which gives 8 : 5, or \${8/5}\$.

### Question 5

Two trains running in opposite directions cross each other in 28 seconds. They, respectively, take 17 and 68 seconds to cross a man standing on the platform. What is the ratio of their speeds?

A

\${11/40}\$.

B

\$1{4/13}\$.

C

\$2{1/6}\$.

D

\$3{5/42}\$.

Soln.
Ans: a

Let the ratio of their speeds by r. If the speed of one train is v, then the speed of the other is rv. By the speed and distance formula, the sum of their lengths is \$(v × 17) + (rv × 68)\$ which should equal the value obtained from the time they take to cross each other,i.e., \$(v + rv) × 28)\$. So \$v × (17 + r × 68\$ = \$v × (1 + r) × 28).\$ Cancelling v and solving for r we get \${11/40}\$.