NIMCET 2023 — Reasoning PYQ

Step-by-step Solution 
1. Convert the speed of the Rajdhani train from $\text{km/h}$ to $\text{m/s}$: [1, 2]  

The speed of the Rajdhani train is given as $54\text{ km/h}$. To convert $\text{km/h}$ to $\text{m/s}$, the speed is multiplied by $\frac{5}{18}$. Speed of Rajdhani train $=54\times \frac{5}{18}=3\times 5=15\text{ m/s}$. [1, 2]  

1. Calculate the length of the Rajdhani train and the platform: 
Let the length of the Rajdhani train be $L\text{ meters}$. The platform length is the same as the train's length, so the platform length is also $L\text{ meters}$. When the train crosses the platform, the total distance covered is the sum of the train's length and the platform's length, which is $L+L=2L\text{ meters}$. The time taken to cross the platform is $36\text{ seconds}$. Using the formula $\text{Distance}=\text{Speed}\times \text{Time}$, it is found that $2L=15\times 36=540\text{ meters}$. Therefore, the length of the Rajdhani train and the platform is $L=\frac{540}{2}=270\text{ meters}$. [2]  

1. Calculate the total distance covered by the Duronto train: 

The length of the Duronto train is $230\text{ meters}$. The Duronto train crosses the same platform, which has a length of $270\text{ meters}$. The total distance covered by the Duronto train is the sum of its length and the platform's length, which is $230+270=500\text{ meters}$. 
1. Calculate the speed of the Duronto train in $\text{m/s}$: 
The time taken by the Duronto train to cross the platform is $25\text{ seconds}$. Using the formula $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$, the speed of the Duronto train is $\frac{500}{25}=20\text{ m/s}$. [2]  

1. Convert the speed of the Duronto train from $\text{m/s}$ to $\text{km/h}$: 

To convert $\text{m/s}$ to $\text{km/h}$, the speed is multiplied by $\frac{18}{5}$. Speed of Duronto train $=20\times \frac{18}{5}=4\times 18=72\text{ km/h}$. 
Final Answer 
The speed of the Duronto train is $72\text{ km/h}$. [1]