Question

the ratio of present ages of rahan and her mother is 2:7 . after 2 year , the ratio of their ages will be 1:3 . what is rehanas present age?​

Answer 1

Given:

The ratio of present age of Rahan and her mother is 2:7

After 2 years, the ratio of the ae will be 1:3

To find:

We need to find the present age of Rahan.

Solution:

The ratio of Rahan and mother age as be represented as "X" and "Y".

Therefore, $\frac{x}{y}$ = $\frac{2}{7}$  ⇒ Equation 1

After 2 years, the age will be 1:3

⇒   $\frac{x.2}{y.2}$ = $\frac{1}{3}$

Now, we will equate the terms

3x + 6 = y + 2

Put $\frac{x}{y}$ = $\frac{2}{7}$  

3. $\frac{2y}{7}$ + 6 = y + 2  

4 = y - $\frac{6y}{7}$

4= $\frac{y}{7}$

= 1y = 28

∴y =28

Put Y = 28 in equation  $\frac{x}{y}$ = $\frac{2}{7}$

Now, we will substitute it and find the answer

​$\frac{x}{28} = \frac{2}{7}$

X = 8.

The Rahan age is 8 and the mother age is 28.

Answer 2

Step-by-step explanation:

Let the present ages of Rehana and her mother be 2x years and 7x years,

respectively.

After 2 years,

Age of Rehana = (2x + 2) years.

Age of Rehana's mother = (7x + 2) years.

It is given that after 2 years, the ratio of their ages will be 1:3.

$\frac{2x + 2}{7x + 2} = \frac{1}{3}$

$= > \: 6x + 6 = 7x + 2 \\ = > \: 7x - 6x = 6 - 2 \\ = > \: x = 4$

=> Rehana's present age=2x=2(4)=8 years.

=> Thus,the present age of Rehana is 8 years.

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