Question

A is two years older than B. A’s father D is twice as old as A and B is twice old as his sister C. The ages of D and C differ by 40 years. Find the ages of A and B. (Ans) 

Answer 1

A = B+2    ,    B=A-2   (1)
D = 2A                       (2)
B = 2C , C=B/2           (3)    
D-C = 40 

2A -B/2 =40                 (STEP 3)     
2A -(A-2)/2 = 40           (STEP 1)

A=26
B=24

Answer 2

Let the age of A be x years.
Let the age of B be y years.
Since, A is two years older than B,
x = y + 2
x - 2 = y........... - (1)
A's father D is twice as old as A,
So, Age of D = 2 x years.
B is twice as old as his sister C.
So, Age of C = 1/2 of age of B, i.e. 1/2y years.
It is also given that, the ages of D and C differ by 40 years.
⇒ 2x  - y/2 = 40
⇒ 4x - y = 80 ...... - (2)
From (1) we have x - 2 = y. So,
4x - (x - 2) = 80
4x - x + 2 = 80
⇒ 3x = 80 - 2
⇒ 3x = 78
⇒ x = 26.
Putting this value in (1) we get,
26 - 2 = y 
⇒ y = 24.
Therefore age of A is 26 and B is 24.