Six years ago the ratio of ages of P and Q was 6 : 5. Four years hence, it will be 11 : 10. What is the age of P now ?

Let say, P and Q's present age is p and q.

So, $$\frac{p-6}{q-6}=\frac{6}{5}.$$

or, $$5p-30=6q-36.$$

or, $$6q-5p=6..................\left(1\right)$$

And, 

$$\frac{p+4}{q+4}=\frac{11}{10}.$$

or, $$10p+40=11q+44.$$

or, $$10p-11q=4...........\left(2\right)$$

Now multiply (1) by 2 and add it to (2) :

$$12q-10p+10p-11q=12+4.$$

or, $$q=16.$$

So, $$p=\frac{6\times16-6}{5}=\frac{90}{5}=18.$$(from eq (1))

C is correct choice.