The correct option is C A= 26 years and B= 24 years
Let age of A=x years
and age of B=y years
Since their age differ by 2 years
x−y=2 (i)
Now.
A's father D is twice as old as A
Age of D=2x years and
B is twice as old as his C
Age of C=12ageofB
=12yyears
Again,
Age of D and C differ by 40 years.
=>2x−y2=40
=>4x−y=80 (ii)
∴ From equation (i) and (ii) we get,
x−y=2 (i)
4x−y=80 (ii)
- + -
−3x=−78
=>x=783
=>x=26 years
Putting the value of x in equation (i) we get,
x−y=2
=>26−y=2
=>−y=−26+2
=>y=24
∴ Age of A is 26 years and Age of B is 24