Question

A train can go from Burdwan to Howrah in $6$ hours and another train can go from Howrah to Burdwan in $4$ hours. Both of them start at $7$A.M. They will meet at

• A. $9.15$ A.M
• B. $9.22$ A.M
• C. $9.24$ A.M
• D. $9.25$ A.M

Answer 1

The correct option is C $9.24$ A.M

Given that,

Two trains start at 7 A.M from their Starting Point

A train $t_1$ goes from from Burdwan to Howrah in 6 Hrs

Another train $t_2$ goes from Howrah to Burdwan in 4 Hrs

They will meet at ?

Step 1

Assume Distance between Burdwan and Howrah as a variable.

Let Distance between Burdwan and Howrah be x km

Step 2

Find the Distance Covered by the trains

Distance Covered by both the trains are equal, as both the trains are moving towards each other.

This Distance is equal to the distance between their Starting point and destination.

Distance Covered by train starting from Burdwan to Howrah = x km

Distance Covered by train starting from Burdwan to Howrah = x km

Step-3

Note the time taken by trains $t_1$ and $t_2$ to cover distance

Time taken by train starting from Burdwan to Howrah $t_1=6hrs$

Time taken by train starting from Burdwan to Howrah $t_2=4hrs$

Step-4

Find the Speed of trains $t_1$and $t_2$

We have,

$speed=\frac{Distance}{time}$

Speed of the train starting from Burdwan to Howrah $s_1=\frac{x}{6}$kmph

Speed of the train starting from Burdwan to Howrah $s_2=\frac{x}{4}$kmph

Step-5

Assume a variable for the time after starting time,for which both the trains are going to meet.

Let both the trains meets 'y' Hrs

Both the trains will meet at time (7+y)$-\left(1\right)$

Step-6

Express the distance covered by both the trains in terms of Speed and time

$distance=speed\times time$

Distance Covered by the trains = (Speed of train $t_1$)y + (Speed of train $t_2$)y

Step-7

Substitute Values to obtain value of y

$⟹x=(\frac{x}{6}y+(\frac{x}{4}y⟹x=x(\frac{y}{6}+\frac{y}{4})⟹y(\frac{5}{12}=1⟹y=\frac{12}{5}hrs$

Step-8

Express y in Mixed Fraction.

Y=$2\frac{2}{5}$ hrs $-\left(2\right)$

Step-9

Express fractional part of Mixed fraction in minutes.

We have,

$⟹\frac{2}{5}hrs=\frac{2}{5}\times 60=24min$

Step-10

Substitute in (2)

Y=$2\frac{2}{5}$hrs = 2 Hours 24 Minutes. $-\left(3\right)$

Step-11

Find the time at which both the trains will meet.

Substituting (3) in (1)

The time at which both the trains will meet = 7 AM + (2 Hours 24 min) = 9 Hours 24 Minutes AM