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Ramesh travels 760km to his home partly by train and partly by car. He takes 8hr, if he travels 160km by train and the rest by car. He takes 12 minutes more, if he travels 240km by train and the rest by car. Find the speed of train and the car.
  1. Speed of train =80km/hr and speed of car =100km/hr
  2. Speed of train =60km/hr and speed of car =120km/hr
  3. Speed of train =40km/hr and speed of car =50km/hr
  4. Speed of train =70km/hr and speed of car =130km/hr

A
Speed of train =40km/hr and speed of car =50km/hr
B
Speed of train =60km/hr and speed of car =120km/hr
C
Speed of train =70km/hr and speed of car =130km/hr
D
Speed of train =80km/hr and speed of car =100km/hr
Solution
Verified by Toppr

Let the speed of train be xkm/hr
and the speed car be ykm/hr respectively.
We know that Speed=DistanceTimeTime=DistanceSpeed
In Case 1
Distance travelled by train = 160km
Distance travelled by car = (760-160)km = 600km
Time taken by train+Time taken by car = 8 hours
Hence the equation becomes
160x+600y=8
In case 2
Distance travelled by train = 240km
Distance travelled by car = (760-240)km = 520km
Time taken by train+Time taken by car = 8 hours+12 minutes
Hence the equation becomes
240x+520y=415......(2)
Hence we get two equations
160x+600y=8.........(1)240x+520y=415......(2)
Let1x=pand1y=q
Hence we get equations
160p + 600q = 8........(3)
240p + 520q = 41/5...(4)
Solving equations (3) and (4)we get p=1/80 and q =1/100
Hencep=1xx=1p=80Similaryy=1q=100
Solving we get x = 80 and y = 100
hence, speed of train =80km/hr and speed of car =100km/hr.

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