# Problems on Trains Quiz Set 009

### Question 1

Two trains running in opposite directions cross each other in 23 seconds. They, respectively, take 19 and 65 seconds to cross a man standing on the platform. What is the ratio of their speeds?

A

\${2/21}\$.

B

\$1{3/20}\$.

C

\$1{21/23}\$.

D

\$2{19/23}\$.

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 × 19) + (rv × 65)\$ which should equal the value obtained from the time they take to cross each other,i.e., \$(v + rv) × 23)\$. So \$v × (19 + r × 65\$ = \$v × (1 + r) × 23).\$ Cancelling v and solving for r we get \${2/21}\$.

### Question 2

A train running at 20km/h leaves a railway station 12 hours later than another train, and meets it in 4 hours. What is the speed of the other train?

A

5 km/h.

B

6 km/h.

C

4 km/h.

D

7 km/h.

Soln.
Ans: a

Let the speed of the train be v km/h. Distance travelled by this train in (4 + 12) hours = 16v km. Equating this to the distance travelled by the second train we get 16v = 20 × 4, which gives v = 5 km/h.

### Question 3

Two trains start simultaneously. The first train moves from Jammu to Tawi, whereas the second train moves from Tawi to Jammu. After they meet at a point in between, they respectively take 16 hours and 36 hours to reach their destinations. What is the ratio of their speeds?

A

\${3/2}\$.

B

\${5/2}\$.

C

\${7/2}\$.

D

\${9/4}\$.

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 \$√36 : √16\$, which gives 6 : 4, or \${3/2}\$.

### Question 4

A train running at a speed of 14m/s crosses a pole in 18sec. How long will it take to cross a platform of length 1008m?

A

90 sec.

B

91 sec.

C

89 sec.

D

92 sec.

Soln.
Ans: a

The length of the train can be obtained from the time it takes to cross the pole. The length of the train = \$14 × 18\$ = 252m. To cross the platform it must travel a total distance equal to the combined lengths of the train and the platform at this speed. So time = \${252 + 1008}/14\$ = 90 seconds.

### Question 5

A train takes 5 hours less if its speed is increased by 12 km/hr. What is the normal speed if the distance is 120km?

A

12.

B

13.

C

11.

D

14.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$120/x\$ - \$120/{x + 12}\$ = 5. This translates to the quadratic equation \$5x^2 + 60x - 1440 = 0\$, which can be solved to obtain x = 12 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value. 