d
\(\begin{array}{l}
No\,of\,divisions\,on\,main\,scale\, = N\\
No\,of\,divisions\,on\,vernier\,scale\, = N + 1\\
Size\,of\,main\,scale\,divisions\, = a\\
Let\,size\,of\,vernier\,scale\,division\,be\,b\,then\,we\,have\\
aN = b\,\left( {N + 1} \right) \Rightarrow b = \frac{{aN}}{{N + 1}}\\
Least\,count\,is\,a - b = a - \frac{{aN}}{{N + 1}}\\
 = a\left[ {\frac{{N + 1 - N}}{{N + 1}}} \right] = \frac{a}{{N + 1}}
\end{array}\)