Question

Ten years from now, Abdul will be twice as old as his son Pavel. Ten years ago, Abdul was seven times as old as Pavel. How old are Abdul and Pavel now?

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• Ten years from now, Abdul will be twice as old as his son Pavel.

• Ten years ago, Abdul was seven times as old as Pavel.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The present ages of Abdul and Pavel

$\bf{\underline{\underline\green{Solution:-}}}$

Let the present age of Abdul be x

And present age of Pavel be y

Ten years from now:-

Age of Abdul = x + 10

Age of Pavel = y + 10

Abdul will be twice as old as his son Pavel.

→ x + 10 = 2( y + 10 )

→ x + 10 = 2y + 20

→ x - 2y = 20 - 10

→ x - 2y = 10.......(i)

Ten years ago:-

Age of Abdul = x - 10

Age of Pavel = y - 10

Abdul was seven times as old as Pavel.

→ x - 10 = 7( y - 10)

→ x - 10 = 7y - 70

→ x - 7y = -70 + 10

→ x - 7y = -60.......(ii)

Subtracting equation (ii) from (i)

→ x - 2y - (x - 7y ) = 10 - (-60)

→ x - 2y - x + 7y = 10 + 60

→ 5y = 70

→ y = 70/5

→ y = 14

Substituting y = 1 in equation (i)

→ x - 2y = 10

→ x - 2(14) = 10

→ x - 28 = 10

→ x = 10 + 28

→ x = 38

Hence;

Present age of Abdul = 38

Present age of Pavel = 14

Answer 2

Given:-

• After 10 Years, Abdul will be twice as old as his son Pavel.

• Ten years ago, Abdul was seven times as old as Pavel.

To Find:-

• Their Present Ages.

Solution:-

Let,

The present age of Abdul be x.

The present age of Pavel be y.

After Ten Years,

Age of Abdul = x + 10

Age of Pavel = y + 10

According To The Question,

→ x + 10 = 2( y + 10 )

→ x + 10 = 2y + 20

→ x - 2y = 20 - 10

→ x - 2y = 10

Before 10 Years,

Age of Abdul = x - 10

Age of Pavel = y - 10

According To The Question,

→ x - 10 = 7(y - 10)

→ x - 10 = 7y - 70

→ x - 7y = -70 + 10

→ x - 7y = -60.

We Got The Final Equation As,

→ x - 2y - (x - 7y ) = 10 - (-60)

→ x - 2y - x + 7y = 10 + 60

→ 5y = 70

→ y = 70/5

→ y = 14

Now, Calculating X.

→ x - 2y = 10

→ x - 2(14) = 10

→ x - 28 = 10

→ x = 10 + 28

→ x = 38

Hence,

• Present age of Abdul = 38.

• Present age of Pavel = 14.