Question

Rampur is 100 km from Sitapur. At 3 pm Bharat Express leaves Rampur for Sitapur and travels at a constant speed of 30 km/ h. One hour later, Laxman Mail leaves Sitapur for Rampur and travels at a constant speed of 40 kmph'. Each train makes one stop only at a station 10 km from its starting point and remains there for 15 min. Which train is nearer to Rampur when they meet?

• A. Both are equidistant
• B. Laxman Mail
• C. Bharat Express
• D. None of these

Answer 1

Answer: (A)

Both are equidistant

Answer 2

Bharat Express travels at 30 km/h and leaves at 3 pm.
Laxman Mail travels at 40 km/h and leaves at 4 pm.
The distance between Rampur and Sitapur is 100 km.
Both trains make a 15-minute stop after covering 10 km.

Now,

By 4 pm (before Laxman Mail starts), Bharat Express has traveled for 1 hour at 30 km/h, covering 30 km.
Then, Bharat Express will stop for 15 minutes at 10 km from Rampur.

At 4 pm, the distance between Bharat Express and Laxman Mail is $100 - 30 = 70$ km.
$\therefore$ both trains are moving towards each other, the combined speed is $( 30 + 40 = 70 )$ km/h.

They meet in $\frac{70}{70} = 1$ hour after 4 pm, i.e., at 5 pm.

Bharat Express travels 30 km from 4 pm to 5 pm, so its total distance covered from Rampur is $30 + 30 = 60$ km.
Laxman Mail travels 40 km from Sitapur by 5 pm.

Therefore, both trains are the equidistant (60 km) from Rampur when they meet.