AB and CD are two chords intersecting at point E. Ram started from point A with a speed of 2km/hr. After reaching point E, Ram moved  to point D with same speed and covered ED in one-fifth of the time taken for AE. Similarly. Shyam moved from point C to point B through point E. If Shyam takes in total 18 hours to cover the whole distance from C to B through point E with same speed. what is the time Shyam took to cover BE?

It is given that Ram covers ED in one-fifth of the time taken for AE, with a 2km/hr constant speed.

It implies, $$\frac{1}{5}\times\ \frac{AE}{2}\ =\frac{ED}{2}$$

$$AE\ =5\times\ ED$$......(1)

Let the speed of Shyam be 's' Kmph. He covers the whole distance from C to B through point E at the same speed in 18 hours.

It implies, $$\frac{CE+BE}{S}=18 Hrs$$.......(2)

From the properties of circles, $$AE\times\ BE=CE\times\ DE$$

$$5DE\times\ BE=CE\times\ DE$$        [From EQ(1)]

$$CE=5BE$$......(3)

From EQ(2) & (3)

$$\frac{5BE+BE}{S}=18$$

$$\frac{6BE}{S}=18$$

$$\frac{BE}{S}=3\ Hrs.$$

Option (C) is the answer.