tcs apti

Question

B moves by taking 3 steps forward and 1 step backward (each step in one second ) 
He walks up a stationary escalator in 118 sec. 
However on moving escalator he takes 40 sec to reach top . Find speed of escalator.   ( 2 Marks )

• A. 1 step/sec
• B. 2 step/sec
• C. 3 step/sec
• D. 4 step/sec

Answer 1

B taking 3 step forward than taking 1 step in backward direction . 
                                 -----------1 sec---------->     -----------2 sec---------->   |  -----------3 sec------------>
                                                                                                       | <----------4 sec-------------

So resultant speed of B = 2 step / 4 second = 1/2 step per second 
when escalator is not moving :
so in 116 seconds it will move 116*(1/2) = 58 steps forward 
B reach at top in 118 seconds so , in next two second B will move 2 step forward . 

so in 118 seconds B will move = 58+2 =60 steps  

when escalator is moving :

Let speed of escaltor is X steps/ second . 
now speed of B with respect to escalator  = (1/2+X) steps/second
now B is reaching at the top in 40 seconds . 

so 60 / (1/2+X) =40 
X=(60/40)-(1/2)=1 steps /second 

So option (A) is correct .