A freight train left Delhi for Mumbai at an average speed of 40 km/hr. Two hours later, an express train left Delhi for Mumbai, following the freight train on a parallel track at an average speed of 60 km/hr. How far from Delhi would the express train meet the freight train?

Correct Answer: Option 240 km

Step-by-Step Explanation:

Step 1: Calculate the distance traveled by the freight train before the express train starts.

The freight train travels at an average speed of 40 km/hr and starts 2 hours before the express train.

Distance covered by the freight train in 2 hours = Speed × Time

$\text{Distance}=40\text{km/hr}\times 2\text{hours}=80\text{km}$

Step 2: Determine the relative speed between the two trains.

Both trains are moving in the same direction (from Delhi to Mumbai).

Freight train's speed = 40 km/hr

Express train's speed = 60 km/hr

Relative speed = Express train speed - Freight train speed

$\text{Relative Speed}=60\text{km/hr}-40\text{km/hr}=20\text{km/hr}$

Step 3: Calculate the time taken for the express train to catch up to the freight train.

The express train needs to cover the initial gap of 80 km at a relative speed of 20 km/hr.

$\text{Time taken}=\frac{\text{Initial Distance Gap}}{\text{Relative Speed}}$

$\text{Time taken}=\frac{80\text{km}}{20\text{km/hr}}=4\text{hours}$

Step 4: Calculate the distance from Delhi where the express train meets the freight train.

The express train travels for 4 hours at a speed of 60 km/hr from Delhi until it meets the freight train.

$\text{Distance from Delhi}=\text{Express Train Speed}\times \text{Time}$

$\text{Distance from Delhi}=60\text{km/hr}\times 4\text{hours}=240\text{km}$

Thus, the express train will meet the freight train at a distance of 240 km from Delhi.