Question

the ages (in year) of varun and tanuj are in the ratio 5:7. if varun was 9 years older tanuj 9 years younger, the age of varun would have been twice the age of tanuj. find the present age of varun and tanuj​

Answer 1

Given :

the ages of varun and tanuj are in the ratio 5:7. if varun was 9 years older tanuj 9 years younger, the age of varun would have been twice the age of tanuj. find the present age of varun and tanuj

Solution :

Let the constant multiple be x

Then,

Let us assume :

Varun's age be 5x

Tanuj's age be 7x

Given that :

Varun is 9 years older than Tanuj

So, 9 years will be added to Varun's age = 5x + 9

Now,

Tanuj is 9 years younger than Varun

We need to substract 9 from Tanuj's present age assumption = 7x - 9

But, here we are given that he would be twice of his age

It means 2 will be multiplied with Tanuj's new age = 2(7x - 9)

Hence, the equation is :

• 5x + 9 = 2(7x - 9)

Substituting, further we get

• 5x + 9 = 14x - 18

• 14x - 5x = 18 + 9

• 9x = 27

Cross multiplying the equation

• x = 27/9

• x = 3

_________________________

Now, finding their present ages :

• Varun's present age = 5x = 5 × 3 = 15 years

• Tanuj's present age = 7x = 7 × 3 = 21 years

Therefore, Varun's age is 15 whereas Tanuj's is 21

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

The ages (in year) of Varun and Tanuj are in the ratio 5:7.

Let assume that

Varun present age be 5x years.

and

Tanuj present age be 7x years.

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: So-\begin{cases} &\sf{Varun \: present \: age \: = \: 5x \: years} \\ \\ &\sf{Tanuj \: present \: age \: = \: 7x \: years} \end{cases}\end{gathered}\end{gathered}$

After 9 years,

Varun age will be 5x + 9 years

9 years ago,

Tanuj age will be 7x - 9 years

According to statement,

If Varun was 9 years older and Tanuj 9 years younger, the age of Varun would have been twice the age of Tanuj.

Thus,

$\rm :\longmapsto\:5x + 9 = 2(7x - 9)$

$\rm :\longmapsto\:5x + 9 = 14x - 18$

$\rm :\longmapsto\:5x - 14x = - 9 - 18$

$\rm :\longmapsto\: - 9x = - 27$

$\rm :\longmapsto\:x = 3$

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: Hence-\begin{cases} &\sf{Varun \: present \: age \: = \: 15 \: years} \\ \\ &\sf{Tanuj \: present \: age \: = \: 21 \: years} \end{cases}\end{gathered}\end{gathered}$

Verification :-

Present age of Varun = 15 years.

Present age of Tanuj = 21 years.

Now,

Varun age after 9 years = 15 + 9 = 24

Tanuj age 9 years ago = 21 - 9 = 12

So, Varun age is twice the Tanuj age.

Hence, Verified