If p + q = 10 and pq = 5, then the numerical value of $$\frac{p}{q}{\text{ + }}\frac{q}{p}$$   will be?

A. 16

B. 20

C. 22

D. 18

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & p + q = 10\,.........{\text{(i)}} \cr & pq = 5 \cr & {\text{Squaring both sides of equation (i)}} \cr & {\left( {p + q} \right)^2} = {\left( {10} \right)^2} \cr & {p^2} + {q^2} + 2pq = 100 \cr & {p^2} + {q^2} + 2 \times 5 = 100 \cr & {p^2} + {q^2} = 90 \cr & {\text{Now,}} \cr & \therefore \frac{p}{q}{\text{ + }}\frac{q}{p} \cr & = \frac{{{p^2} + {q^2}}}{{pq}} \cr & = \frac{{90}}{5} \cr & = 18 \cr} $$