Question

$\huge\red{\boxed{\sf QuEStiON}}$

A and B are friends and their ages differ by two years. A’s father D is twice as old as A, & B is twice as old as his sister C. The ages of D and C differ by 40 years. Find the ages of A and B?​

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 =

2

y

years.

Clearly, D is older than C

2x−

2

y

=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=

3

82

=27

3

1

Putting x=

3

82

in equation (iii), we get

y=

3

82

+2=

3

88

=29

3

1

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

or

A's age =27

3

1

years and B's age =29

3

1

years.

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Answer 2

Answer:

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