A body is performing simple harmonic with an amplitude of 10cm ....

In SHM, velocity of the particle at any displacement, $x$ is given by, $v = \sqrt{{A}^{2} - {x}^{2}}$.

Therefore,

$⇒ \dfrac{v}{3v} = \dfrac{\left(\sqrt{{A}_{1}^{2} - 25}\right)}{\sqrt{{A}_{2}^{2} - 25}}$ $⇒ \sqrt{{A}_{2}^{2} - 25} = 3 \times \sqrt{75}$

$⇒ {A}_{2}^{2} = 700$ $⇒ {A}_{2} = \sqrt{700}cm$