Q.

Mohan takes 8 seconds to go up a certain escalator going up, while Sohan takes 12 seconds to go down the same escalator. If Sohan takes 3 steps for every 2 steps that Mohan takes, how long will Sohan take to go up the same escalator?

Assume Sohan’s speed remains same whether he goes up the escalator or down the escalator.

A. 2.4 sec

B. 4 sec

C. 4.8 sec

D. 6 sec

Ratio of speeds of Sohan and Mohan is given. Assume speeds of Sohan, Mohan and Escalator in terms of variables and write the two equations for they taking 8 secs and 12 secs.

Solve simultaneously to get relation between the speeds of the individuals and that of the escalator.

Now knowing escalators speed wrt to Sohan’s speed, it is simple proportionality between time and speed.

D. 6 sec

Since ratio of speeds of Sohan to Mohan is 3 : 2, say speeds are 3k and 2k respectively.

And let speed of escalator be n.

Mohan taking 8 secs to go up the up-escalator …

D = (2k + n) × 8

Sohan taking 12 secs to go down the up-escalator …

D = (3k – n) × 12

Solving simultaneously,

16k + 8n = 36k – 12n

n = k

Sohan takes 12 secs at a speed of (3k – k) i.e. 2k

How much will he take at a speed of (3k + k) i.e. 4k?

6 seconds.