Question

A passenger sitting in a train of a certain
length which is running at a speed of 60 km/hr
passing through two bridges. the notices that be
crossed the first bridge and second bridge in time
intervals which are in the ratio of 7:4 respectively.
If the length of the first bridge is 350m, then the
length of the second bridge is
1. 210m
2. 220m
3. 200 m
4. 190m
5. 180m

Answer 1

Given :

Speed of train:

$= 60 \: \frac{km}{hr}$

Ratio of time intervals on crossing two bridges= 7 : 4.

Length of first bridge = 350 m

To find :

Length of second bridge,

Solution:

Speed = It is the quantity to measure the distance covered by an object per unit time.

In this case, speed given is :

$= 60 \: \frac{km}{hr}$

It is also given that the time ratio of crosaing of two bridges is = 7 : 4

So lets think,

Time taken to cross first bridge is = 7x

and time taken to cross second bridge = 4x.

(so that the ratio is 7 : 4)

The formula of speed :

$\bf \: v = \frac{d}{t}$

(equation 1l

where

v = speed of object

d = distance covered by object.

t = time taken by object.

In case of crossing first bridge

v = 60 km per hour (given)

d = 350 m (given)

t = 7x (ratio given)

So putting all values in equation 1, we get :

$60 = \frac{350}{7 \times x } \\ 60 = \frac{50}{x}$

so,

$x = \frac{50}{60} = \frac{5}{6}$

we know that time taken to cross second bridge = 4x

speed of train = 60 km per hour

So putting the values of speed and time,

For the length of bridge,

$60 = \frac{l}{( \frac{5 \times 4}{6} )} \\ 60 = \frac{6l}{20} \\ so \\ 6l = 60 \times 20 = 1200$

so,

$l = \frac{1200}{6} = 200m$

so,

The length of second bridge = 200 m.

(option 3)

Answer 2

Given :

Speed of train: $=60 km/hr$

Ratio of time intervals on crossing two bridges$= 7 : 4.$

Length of first bridge $= 350 m$

To find : Length of second bridge,

Solution:

Speed = It is the quantity to measure the distance covered by an object per unit time.

In this case, speed given is =  $60km/hr$

It is also given that the time ratio of crossing of two bridges is $= 7 : 4$

So lets think,

Time taken to cross first bridge is $= 7x$

and time taken to cross second bridge $= 4x.$

(so that the ratio is $7 : 4$)

The formula of speed $v=\frac{d}{t}$

(equation 1l

where

v = speed of object

d = distance covered by object.

t = time taken by object.

In case of crossing the first bridge

$v = 60 km$ per hour (given)

$d = 350 m$ (given)

$t = 7x$ (ratio given)

So putting all values in equation 1, we get :

$60=\frac{350}{7\times x}$

$60=\frac{50}{x}$

so,

$x=\frac{50}{60}=\frac{5}{6}$

we know that time taken to cross second bridge $= 4x$

speed of train $= 60 km$ per hour

So putting the values of speed and time,

For the length of bridge,

$60=\frac{l}{\frac{5\times 4}{6} }$

$60=\frac{6l}{20}$

so,

$6l=60\times 20=1200$

so,

$l=\frac{1200}{6}=200m$

The length of second bridge $= 200 m.$

(option 3)

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