Question

Max is as twice as old an jane. Five years ago his age was thrre time of jane's age. Find thir present ages

Answer 1

Solution :

• Let the present age of Max be 'x'
• And Present age of Jane be 'y'

We know that Max is twice as old as Jane.

• ∴ x = 2y ------ (1)

5 years ago,

• Max = (x - 5)
• Jane = (y - 5)

It is given that Max was 3 times Jane.

• ∴ (x - 5) = 3 (y - 5)

Substituting the value of 'x', Eq (1):

⟹ (2y - 5) = 3 (y - 5)

⟹ (2y - 5) = (3y - 15)

⟹ 3y - 2y = 15 + 5

⟹ y = 10

Substituting 'y' value in Eq (1) :

⟹ x = 2y

⟹ x = 2 (10)

⟹ x = 20

• ∴ Max is 10 years old and
• Jane is 20 years old.

Answer 2

Correct question:

Max is as twice as old as Jane. Five years ago his age was three time of Jane's age. Find there present ages

To find:

$\to$The present age of Max and Jane

Information given in the question:

• Max is as twice as old an Jane
• Five years ago his age was three time of Jane's age

Solution:

Let,The age of Max be $\mathsf{x \ years}$ and the age of Jane be $\mathsf{y \ years}$

So,Max is as twice as old an Jane

From these we can write,

$\to \boxed{\mathsf{y=2x}} \ - \ \mathsf{Equation :1}$

So,Five years ago his age was three time of Jane's age

From these we can write,

$\to \mathsf{(y-5)=3(x-5)} \\\\\to \mathsf{y - 5 = 3x-15}\\\\\to \mathsf{or,y=3x-15+5}\\\\\to \mathsf{or,} \boxed{\mathsf{y=3x-10}} \mathsf{ \ - \ Equation :2}$

Now,Putting $\mathsf{y=3x-10}$ in Equation : 1

$\to \mathsf{3x-10=2x}\\\\\to \mathsf{or,3x--2x=10}\\\\\to \mathsf{or,x=10}$

Now,Putting $\mathsf{x=10}$ in Equation : 1

$\to \mathsf{y=2*10}\\\\\to \mathsf{or,y=20}$

Answer:

The age of Max=$\mathsf{10 \ years}$

The age of Jane=$\mathsf{20 \ years}$