Hello, vritikagupta!

This is topsquark's solution . . . with a diagram.

A carom board (4ft*4ft sq) has the queen at the centre.

The queen, hit by the striker, moves to the front edge, rebounds,

and goes in the hole behind the striking line.

Find the magnitude of displacement of the queen

(A) from to the centre to the front edge

(B) from the front to the hole

(c) from the centre to the hole.

Make a sketch and you can almost "eyeball" the problem! Code:

2 B C D
* - - - - - - - - * - - * - - - - - *
| : θ/ \θ |
| 2: / \ |
| : / \ |
| : / \ |
| :/ \ |
| A* \ |4
| \ |
| \ |
| \ |
| \ |
| \|
* - - - - - - - - - - - - - - - - - *E

Since the angle of incidence (θ) equals the angle of reflection,

. . ∆ABC ~ ∆CDE

Then .BC:CD .= .BA:DE .= .2:4 .= .1:2

Since BD = 2, we have: .BC = 2/3, .CD = 4/3

Then: AC˛ .= .AB˛ + BC˛ .= .2˛ + (2/3)˛ .= .40/9

. . . . . . . . . . . . . . .__

. . Hence: .AC .= .2√10/3 . **(A)**

. . . . . . . . . . . . . . . . . __

And: .CE .= .2·AC .= .4√10/3 . **(B)**

. . . . . . . . . . . . . . .__

And: .AC + CE .= .6√10/3 . **(C)**