Question

A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the ends nearest to the cow. Seeing this cow ran towards the the train and managed to escape when the train was 2m away from bridge. If it had run in the opposite direction, it would hit by the train 2m before the end of the bridge. What is the lenght of the bridge in meters assuming the speed of the train is 4 times that of cow ?
A) 22 mts
B) 28 mts
C) 32 mts
D) 34 mts

Answer 1

the answer is option B

Answer 2

Option c

ANSWER:

A cow was standing on a bridge. The length of the bridge is 32 meters. So option c is correct.

SOLUTION:

Given, a cow was standing on a bridge, 5m away from the middle of the bridge.  

Let the length of the bridge be "x" meters.

Then, distance between cow and starting point of nearest end of bridge  $=\frac{x}{2}-5 \text { meters }$

A train was coming towards the bridge from the ends nearest to the cow.  

The speed of the train is 4 times that of cow.

Let the speed of the cow be s, then speed of the train becomes "4s".

And the distance between train and bridge be y meters.

Seeing this cow ran towards the train and managed to escape when the train was 2m away from bridge.

In this instance, time taken by train and cow will be same, with reference to common frame.

Time taken by train = time taken by cow

$\frac{\text {distance travelled by train}}{\text {speed of train}}=\frac{\text {distance travelled by cow.}}{\text {speed of cow}}$

Distance travelled by train= y – 2 because, when cow left the bridge, train is 2 m away. Hence we get,

$\frac{y-2}{4 s}=\frac{\frac{x}{2}-5}{s}$

$y-2=4\left(\frac{x}{2}-5\right)$

y – 2 = 2x – 20

2x – y – 20 + 2= 0

2x – y – 18 = 0 → (1)

Now, If it had run in the opposite direction, it would hit by the train 2m before the end of the bridge.

Here again time taken by train = time taken by cow.

$\begin{array}{l}{\frac{d i s t a n c e \text { travelled by train}}{\text { speed of train }}=\frac{d i s t a n c e \text { travelled by cow. }}{\text { spesd of cow }}} \\\\ {\frac{y+x-2}{4 s}=\frac{(x-2)-\left(\frac{x}{2}-5\right)}{s}} \\\\ {x+y-2=4\left(x-\frac{x}{2}+5-2\right)} \\\\ {x+y-2=4\left(\frac{x}{2}+3\right)}\end{array}$

x + y – 2 = 2x + 12

2x – x – y + 12 + 2 = 0

x – y + 14 = 0 → (2)

Now, subtract (2) from (1) , we get

x + 0 – 32 = 0

x = 32

Hence, the length of the bridge is 32 meters. So option c is correct.