A train leaves station A at 8 am and reaches station B at 12 noon. A car leaves station B at 8:30 am and reaches station A at the same time when the train reaches station B. At what time do they meet ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 10:08 am
Given :
Train leaves station A at 8 am
Car leaves station B at 8 : 30 am
Formula used :
Speed = Distance/Time ------ (1)
Calculations :
Let the total distance between station A and B be x
Time taken by train to cover x km = 4 hours
Time taken by car to cover x km = 3.5 hours
Using equation (1)
Speed of train = (x/4) kmph
Speed of car = (2x/7) kmph
Distance covered by train in half an hour (8 : 30 am) = (x/4) × (1/2)
⇒ x/8 km
Remaining distance = x - x/8 = 7x/8 km
Let y be the time after which they will meet eachother
⇒ (x/4) × y + (2x/7) × y = 7x/8
⇒ (7x + 8x)/28y = 7x/8
⇒ 15x/28y = 7x/8
⇒ y= 49/30 hours
⇒ y = (49/30) × (60)
⇒ y = 98 mins or 1 hour 38 mins
Hence, both train and car will meet eachother at
⇒ 8 : 30 am + 1 hour 38 mins
⇒ 10 : 08 am