Question

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


A​

Answer 1

Let the ages of A and B be x and y years respectively. Then,

x−y=±2 [Given]

D's age =2x years and, C's age =y/2 years

Clearly, D is older than C

2x− y/2 =40⇒4x−y=80

Thus, we have the following two systems of linear equations

x−y=2 .(i)

and, 4x−y=80 (ii)

or

x−y=−2 (iii)

and, 4x−y=80 ..(iv)

Substracting equation (i) from equation (ii), we get

3x=78⇒x=26Putting x=26 in equation (i), we get y=24

or

Substracting equation (iv) from equation (iii), we get

−3x=−82⇒x=82/3 = 27⅓

Putting x= 82/3 in equation (iii), we get

y= 82/3 +2=88/3 =29 ⅓

Hence, A's age =26 years and B's age =24 years

or

A's age =27 ⅓ years and B's age =29 ⅓ years.