Question

Two trains of equal length are running on parallel lines in the same direction at 78 km/hr and 68 km/hr. The faster train passes the slower train in 72 seconds. The length of each train is:
A) 100 m
B) 160 m
C) 180 m
D) 140 m
E) None of these

Answer 1

Answer:

Suppose the length of train = x meter

Relative velocity of trains = (78-68) km/hr = 10 km/hr = 50/18 m/s

total distance covered by faster train in 72 seconds = 2x meter

according to question,

(2x/72) = 50/18

x=100 meter

Hence the length of each train is 100 meter

Option (A)

Answer 2

Answer:

The correct option: E) None of these

Step-by-step explanation:

• Train A is the faster train.

         Its speed = 78 km/hr = $\frac{78*1000}{3600}$ m/s = $\frac{195}{9}$ m/s.

         Time = 72 s

          Covered distance = speed × time =  $\frac{195}{9}$ × 72

                                                                   = 195 × 8 = 1560 m.

• Train B is the slower train.

         Its speed = 68 km/hr = $\frac{68*1000}{3600}$ m/s = $\frac{170}{9}$ m/s.

         Time = 72 s

          Covered distance = speed × time =  $\frac{170}{9}$ × 72

                                                                   = 170 × 8 = 1360 m.

• Length of train A = Length of train B

                                    = Distance covered by A - distance covered by B

                                    = 1560 m - 1360 m

                                    = 200 m.

• Conclusion: The length of each train is 200m. As 200m is not mentioned in any option. So the correct answer will be E) None of these.