Aman is currently 20 years older than his oldest son. his oldest son is currently two years older than his youngest son. three years from the current time, the products of the ages of his sons will be ten more than eleven times the age of the father. what is the current age of man's youngest son?

Hello,
Let's f the age of the father
a the age of the oldest son
y the age of the youngest son

f=a+20
a=y+2  ==>f=y+22

In 3 years:  father->f+3=y=25
oldset son ->a+3=y+5
youngest son->y+3

Product of the ages of the sons in 3 years: (y+5)(y+3)=y²+8y+15

so y²+8y+15=11(y+25)+10
==>y²+8y+15=11y+275+10
==>y²-3y-270=0
Δ=9+4*270=1089=33²

y=(3+33)/2=18 or (y=(3-33)/2 <0 to exclude)

The youngest son is 18 years's old