A man travels 840 km in 12 hours, partly by train and partly by car. If he had travelled all the way

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18 Apr 2022 Time Distance & Speed

A man travels 840 km in 12 hours, partly by train and partly by car. If he had travelled all the way by train, he would have saved 1/4 of the time he would have taken to travel by car only and would have arrived at his destination 1 hour 30 minutes early. Find the distance he covered while travelling by car.

OPtion

1) 480 km
2) 380 km
3) 520 km
4) 540 km
5) 420 km
6) 360 km
7) 600 km
8) 270 km
9) 300 km
10) None of these

Solution

Total Distance = 840 km.
Total Time taken by Train and Car = 12 Hours
By travelling all the distance by train, he would have reached 1.5 hrs early i.e. He would have taken 12 - 1.5 = 10.5 hrs.
.'. Speed of the train = 840/10.5 = 80 kmph
Time taken by train to travel 840 km = (1 - 1/4)* Time taken by car to travel 840 km = 10.5
⇒ Time taken by car to travel 840 km = 10.5/(3/4) = 14 hrs
.'. Speed of car = 840/14 = 60 kmph
Let the distance covered by car = x km and by train = (840-x) km
Then, x/60 + (840-x)/80 = 12
Solving, we get x=360 km

Correct Option: 6 Best Solution (1)

Mayank Kandoi   2 years AGO

Time taken by train only = 12 - 1.5 = 10.5 hours
Time taken by car only = 10.5 × 4/3 = 14 hours

Speed of train = 840/10.5 = 80 kmph
Speed of car = 840/14 = 60 kmph

Let partial time (t hours) is taken by train.
So partial time taken by car is (12-t hours)
Speed × Time = Distance
80t + 60 (12-t) = 840
t = 6 hours

Partial time taken by car = 12-6 = 6 hours
Speed = 60 kmph
Distance = 60×6 = 360 km

Option 6

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