The distance moved by the tip of the hand in clock. The minute hand of a clock is $15$ cm
  long. The distance moved by the tip
  of the hand in $35$ minutes is


$a.)\ 35\pi \\
\color{green}{b.)\ \dfrac{35\pi}{2}} \\
c.)\ \dfrac{5\pi}{4} \\
d.)\ \dfrac{5\pi}{2} $

For minute hand,

$12\ hrs =360^{\circ} \\
35\ min=\left(\dfrac{35}{2}\right)^{\circ} $

Distance$=\dfrac{2\pi 15\times 35}{360\times 2}=\dfrac{35\pi}{24}\ cm $

But that is not in options 

I look for a short and simple way.

I have studied maths upto $12th$ grade.
It has moved $\frac{35}{60}$ of a full circle (a full circle consists of $60$ minutes, and it has moved $35$ of those). A full circle is $2\pi\cdot15cm=30\pi cm$. It has therefore moved a total of
$$
\frac{35}{60}\cdot30\pi cm=\frac{35\pi}{2}cm
$$
Your mistake ? You are missing one fact, the minute hand has already went through $\left(360\cdot 12\right)^{\circ}$ every 12 hours.