A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. the age of D and C differ by 40 years. find the ages of A and B.

Let the ages of A = x years

and

age of B = y years.

Since, their ages differ by 2 years.

x - y =2 (Assuming A is older than B) -------------------(i)

Now, A's father D is twice as old as A,

Age of D = 2x years.

and

B's is twice as old as his C,

Age of C =

Also, the ages of D and C differ by 40 years.

∴On solving equations (i) and (ii) , we get,

Put the value of x in (i) we get

⇒ 26 - 2 = y

⇒ **y = 24 years = B's age**

∴Age of **A is 26 years** and **B is 24 years.**

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