c
(c) Comparing with $y = a\cos (\omega t + kx - \phi )$,
We get $k = \frac{{2\pi }}{\lambda } = 0.02\, \Rightarrow \,\lambda = 100\,cm$
Also, it is given that phase difference between particles $\Delta \phi = \frac{\pi }{2}.$
Hence path difference between them
$\Delta = \frac{\lambda }{{2\pi }} \times \Delta \phi = \frac{\lambda }{{2\pi }} \times \frac{\pi }{2} = \frac{\lambda }{4} = \frac{{100}}{4} = 25\,cm$