Question

Q.19. A train travels 288 km at a uniform speed. If the
speed had been 4 km/hr. more, it would have taken
1 hour less for the same journey, find the speed of
the train.
(A) 30 kmph (B) 36 kmph
(C) 32 kmph (D) 34 kmph
TOS​

Answer 1

Answer:

• Option (b) 36kmph

Step-by-step explanation:

Let , the uniform speed of train = ‘s’ km/h

and the time taken to cover 288km = ‘t’ hrs

We know that,

→ Speed = Distance/Time

→ s = 288/t

→ st = 288 ___(1)

If the speed of the train increased by 4km/h

then , it's speed = ‘s + 4’ km/h

and time taken to cover same distance= ‘t - 1’ hrs

We know that ,

→ Speed = Distance/Time

→ s + 4 = 288/(t - 1) ___(2)

→ (t - 1)(s + 4) = 288

Substituting 288 = st from equation (1)

→ st + 4t - s - 4 = st

→ st + 4t - s - 4 - st = 0

→ 4t - s - 4 = 0

→ 4t - 4 = s

→ 4(t - 1) = s

→ t - 1 = s/4 ___(3)

Substituting the value of t - 1 = s/4 in equation (2)

→ s + 4 = 288/(t - 1)

→ s + 4 = 288/(s/4)

→ s + 4 = 1152/s

→ s(s + 4) = 1152

→ s² + 4s = 1152

→ s² + 4s - 1152 = 0

→ s² + 36s - 32s - 1152 = 0

→ s(s + 36) - 32(s + 36) = 0

→ (s - 32) (s + 36) = 0

→ s - 32 = 0 OR s + 36 = 0

→ s = 32 OR s = -36

So , we get speed s = 32 , -36

As speed cannot be negative so,

→ s = 32

We know that ,

→ Speed of train = s + 4

→ Speed of train = 32 + 4

→ Speed of train = 36

Therefore , speed of train = 36 kmph

So, option (b) is correct