A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is

Correct Answer: 275 m

Step-by-Step Explanation:

Step 1: Find the length of the first train
Let the length of the first train be $L_1$ and its speed be $S_1$.

Given speed of the first train:
$S_1=72\text{km/hr}$

Convert the speed from km/hr to m/s by multiplying by $\frac{5}{18}$:

$S_1=72\times \frac{5}{18}=20\text{m/s}$

The time taken by the first train to cross a post is $t_1=20\text{seconds}$.
When a train crosses a post, the distance travelled equals the length of the train ($L_1$).

$L_1=S_1\times t_1$

$L_1=20\times 20=400\text{m}$

Step 2: Find the length of the second train
Let the speed of the second train be $S_2$ and its length be $L_2$.

Given speed of the second train:
$S_2=54\text{km/hr}$

Convert this speed to m/s:

$S_2=54\times \frac{5}{18}=15\text{m/s}$

Since both trains are travelling in the same direction, their relative speed ($S_{\text{rel}}$) is the difference between their speeds:

$S_{\text{rel}}=S_1-S_2=20-15=5\text{m/s}$

The time taken to completely cross each other is 1 minute 45 seconds.
Convert time into seconds:
$t_2=1\text{min}45\text{sec}=60+45=105\text{seconds}$

When one train crosses another, the total distance covered is the sum of their lengths ($L_1+L_2$):

$L_1+L_2=S_{\text{rel}}\times t_2$

$400+L_2=5\times 105$

$400+L_2=525$

$L_2=525-400=125\text{m}$

Step 3: Calculate the difference in length between the two trains

$\text{Difference}=L_1-L_2$

$\text{Difference}=400-125=275\text{m}$

Hence, the difference in length between the two trains is 275 m.