The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is :

Answer: Option A

The required number = Number of numbers, which are (divisible by 3 + divisible by 7 - divisible by 21)
Number of number divisible by 3,
$$\begin{array}{rl}& \text{ = }\frac{198-3}{3}+1\\ & =66\end{array}$$
Number of number divisible by 7
$$\begin{array}{rl}& =\frac{196-7}{7}+1\\ & =28\end{array}$$
Number of number divisible by 21,
$$\begin{array}{rl}& =\frac{189-21}{21}+1\\ & =9\end{array}$$
Thus, the divisible value
$$\begin{array}{rl}& =66+28-9\\ & =85\end{array}$$
Thus, number of numbers which are not divisible by 3 or 7
$$\begin{array}{rl}& =200-85\\ & =115\end{array}$$