Question

Four persons K, L, M and N are initially at the corners of a square of side of length d. If every person starts moving, such that K is always headed towards L, L towards M, M is headed directly towards N and N towards K, then the four persons will meet after (assume that they move with a constant speed v)

• A.
• B.
• C.
• D.

Answer 1

The correct option is A. .

It is obvious from considerations of symmentry that at any moment of time all of the persons will be at the corners of square whose side gradually

decreases (see fig.) and so they will finally meet at the centre of the square O.

The speed of each person along the line joining his inital position and O will be $vcos{45}^o$ = $\frac{v}{\sqrt{2}}$ to reach the centre.

The distance covered by each person is $dcos{45}^o=\frac{d}{\sqrt{2}}$

The four persons will meet at the centre of the dquare O after time $t=\frac{Distance}{Speed}$.
$\therefore$ t = $\frac{\frac{d}{\sqrt{2}}}{\frac{v}{\sqrt{2}}}$ = $\frac{d}{v}$.