Question

sanjay is now 1/2 as old as his brother. in 6 more years he will be 3/5 as old as his brother then. what is the present age of each boy​

Answer 1

Answer:

Let us assume the present age of Sanjay’s brother =x

…...… (1)

Then from the statement in question we have the present age of Sanjay is 12

times the age of his brother

⇒

Present age of Sanjay =x2

…...… (2)

Now we have to find the equation of age of Sanjay and his brother after 6 years.

After six years, the age of Sanjay’s brother will be the present age of Sanjay’s brother plus 6 years.

From equation (1):

⇒

Age of Sanjay’s brother after 6 years =x+6

………..… (3)

Age of Sanjay after six years will be the present age of Sanjay plus 6 years.

From equation (2):

⇒

Age of Sanjay after 6 years =x2+6

………..… (4)

We know from the statement of the question that after six years, the age of Sanjay is 35

times the age of his brother.

We use equations (3) and (4) to write this relation, i.e.

⇒(x2+6)=35(x+6)

Take LCM on LHS of the equation and multiply the fraction to bracket in RHS of the equation

⇒x+122=3x+185

Cross multiply the equations on both sides

⇒5(x+12)=2(3x+18)

Multiply the terms inside the bracket

⇒5x+60=6x+36

Shift all constant values to one side of the equation

⇒60−36=6x−5x

⇒24=x

So, the present age of Sanjay’s brother is 24 years.

From equation (2), present age of Sanjay =x2

Substituting the value of x as 24,

⇒

Present age of Sanjay =242

⇒

Present age of Sanjay =12

So, the present age of Sanjay is 12 years.