A clock shows 3:00. After how many minutes will the angle between the hands be 60° ?

We know the angle between hour hand and minute hand is given by the formula: $$\left|30h-\dfrac{11m}{2}\right|$$
Here, $$h=3$$
So, either, $$30h-\dfrac{11m}{2}=60$$
or, $$30\times\ 3-\dfrac{11m}{2}=60$$
or, $$\dfrac{11m}{2}=30$$
or, $$m=\dfrac{60}{11}=5\ \dfrac{5}{11}$$

Or,$$\dfrac{11m}{2}-30h=60$$
or, $$\dfrac{11m}{2}-30\times\ 3=60$$
or, $$\dfrac{11m}{2}=60+90=150$$
or, $$m=\dfrac{150\times\ 2}{11}=\dfrac{300}{11}=27\ \dfrac{3}{11}$$

Amongst the given options, option C is the correct answer.