8
Q:

# Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was

 A) 2:1 B) 3:2 C) 4:3 D) 5:4

Explanation:

Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)

Therefore, Ratio of the speeds of two trains = $\inline \sqrt{9}:\sqrt{4}$ = 3 : 2

Q:

Two goods trains each 520 m long, are running in opposite directions on parallel tracks. Their speeds are 42 km/hr and 36 km/hr respectively. Find the time taken by the slower train to cross the driver of the faster one ?

 A) 60 sec B) 48 sec C) 45 sec D) 34 sec

Explanation:

Relative speed = 42 + 36 = 78 km/hr = $\inline \fn_jvn \small \frac{65}{3}$ m/s
Distance = (520 + 520) =1040 mts.
Time = $\inline \fn_jvn \small 1040\times \frac{3}{65} sec$= 48 sec

4 107
Q:

Two trains are running at 60 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 seconds. What is the length of the fast train ?

$\inline \fn_jvn \small A) 66\tfrac{2}{3} mts$  $\inline \fn_jvn \small B)66 \tfrac{3}{2} mts$  $\inline \fn_jvn \small C) 63\tfrac{4}{5} mts$  $\inline \fn_jvn \small D)63 \tfrac{5}{4}mts$

 A) Option A B) Option B C) Option C D) Option D

Explanation:

As Trains are moving in same direction,
Relative Speed = 60-20 = 40 kmph
$\fn_jvn&space;\small&space;\Rightarrow$ $\inline \fn_jvn \small 40\times \frac{5}{18} = \frac{100}{9}$ m/sec

Length of Train= Speed * Time

Length = $\inline \fn_jvn \small \frac{100}{9}\times 6$

$\fn_jvn&space;\small&space;\Rightarrow$ $\inline \fn_jvn \small \frac{200}{3} =66 \tfrac{2}{3} mts$

5 98
Q:

Length of train is 170 meters and speed of train is 63 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

 A) 355 mts B) 325 mts C) 365 mts D) 312 mts

Explanation:

Given speed = 63 km/hr = $\inline \fn_jvn \small 63\times \frac{5}{18}=\frac{35}{2}$ m/s
Let the length of the bridge = x mts
Given time taken to cover the distance of (170 + x)mts is 30 sec.
We know speed = $\inline \fn_jvn \small \frac{distance}{time}$ m/s

$\fn_jvn&space;\small&space;\Rightarrow$ $\inline \fn_jvn \small \frac{35}{2}=\frac{170+x}{30}$

$\fn_jvn&space;\small&space;\Rightarrow$ x = 355 mts.

4 81
Q:

A train running at the speed of 40 km/hr crosses a signal pole in 9 seconds. Find the length of the train ?

 A) 90 mts B) 150 mts C) 120 mts D) 100 mts

Explanation:

We know that   $\inline \fn_jvn \small speed = \frac{distance}{time}$

$\fn_jvn&space;\small&space;\Rightarrow$ distance= speed * time
$\fn_jvn&space;\small&space;\Rightarrow$ d = $\inline \fn_jvn \small 40\times \frac{5}{18}\frac{mts}{sec}\times 9$

$\fn_jvn&space;\small&space;\Rightarrow$  d= 100 mts.

4 102
Q:

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is :

 A) 9.5 km/hr B) 10 km/hr C) 10.5 km/hr D) 11 km/hr

$\inline&space;\therefore$ Man's rate against the current = (12.5 - 2.5) = 10 km/hr.