Select the option that is related to the fourth term in the same way as the first term is related to the second term.
16 : 272 :: ? : 380

$$\left(16\right)^2+16\ =\ 256+16\ =\ 272$$

Lets's assume 'y' in place of the question mark.

$$(y)^2+y  = 380$$

y(y+1) = 380

Now check each of the options one by one by putting the value of 'y' in the above equation.

Option (a) 21

y(y+1) = 380

$$21\times22 = 380$$

$$462\ne\ 380$$

Option (b) 19

y(y+1) = 380

$$19\times20 = 380$$

380 = 380

The given equation is satisfied. So this will be the correct answer.
Option (c) 23

y(y+1) = 380

$$23\times24 = 380$$

$$552\ne\ 380$$

The given equation is not satisfied. So this will not be the correct answer.

Option (d) 17

y(y+1) = 380

$$17\times18 = 380$$

$$306\ne\ 380$$

The given equation is not satisfied. So this will not be the correct answer.