Time taken by a person walks from A to M at p km/h and from M to B at 2q km/h is the same as if he had travelled at the uniform rate of 3r km/h, he could have walked from A to B and back again. If AM : BM = 1 : 2 then :

$\frac{2}{r}=\frac{1}{p}+\frac{1}{q}$

Time = \(\frac{Distance }{Speed}\)

Time taken from A to M = (\frac{1 }{p}\)

Time taken from M to B = (\frac{1 }{q}\)

ATQ,

(\frac{1 }{p}\) + (\frac{1 }{q}\) = (\frac{3 }{3r}\)

(\frac{1 }{p}\) + (\frac{1 }{q}\) = (\frac{1 }{1r}\)

The correct answer is option (2) : $\frac{2}{r}=\frac{1}{p}+\frac{1}{q}$