**Question:**

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is : A. 45 m B. 50 m C. 54 m D. 72 m

B

B) 50m is correct

D

Pls Can anyone explain how you got C.

__C__

C

B. 50 m

Let the length of the train be 'D' .

Let the speed of the train be 'x' m/sec.

Consider the two conditions

PERSON 1

speed = 2 km/hr = 2*5/18 = 5/9 m/sec .

Effective speed =( x - 5/9) m/s .

time taken to overtake = 9 sec .

Dist = time * speed

D = 9 * (x - 5/9)

= 9x - 5 . -(A)

PERSON 2

speed = 4 km/hr = 4* 5/18 = 10/9 m/s.

Effective speed = ( x- 10/9) m/s .

time taken = 10 sec.

D = 10 ( x - 10/9)

= 10/9 (9x-10). - (B)

(A) = (B)

(9x -5 ) = 10/9 ( 9x - 10) .

9(9x - 5 ) = 10 (9x -10)

81x - 45 = 90x - 100 .

9x = 55.

x = 55/9 m/s or 55/9 *(18/5) = 22 km/hr.

Substituting this in (A)

we get , D = (9x - 5)

D = [9*(55/9) - 5 ]

= 55 - 5

= 50 m .

__Ç__

__C__

Pls explain