In a ΔABC, If 2∠A = 3∠B = 6∠C, then the value of ∠B is:

Answer: Option A

According to question,
Given :
$$\begin{array}{rl}& 2\angle A=3\angle B\\ & \frac{\angle A}{\angle B}=\frac{3}{2}3\angle B=6\angle C\\ & \frac{\angle B}{\angle C}=\frac{6}{3}=\frac{2}{1}\end{array}$$
To make angle ∠B same
∴ ∠A     :     ∠B     :     ∠C
      3     :        2     :     1
As we know that
∠A + ∠B + ∠C = 180°
3x + 2x + x = 180°
x = 30°
∠B = 2x
∠B = 60°