Question

the present age of Sujatha's mother is two more than twice the age of Sujatha. After 6 years , the ratio of the ages of the mother and Sujatha will be 24:13 .Find their present ages​

Answer 1

Given:- Present age of Sujatha's mother is twice the age of Sujatha.

After six years, the ratio of ages of the mother and Sujatha will be 24:13

To Find:- Present ages of Sujatha and her mother

Solution:- Let the present age of Sujatha be x and her mother be y.

So, $y= 2x+2$  --------------------(a) (Given)

And, $\frac{24}{13}=\frac{y+6}{x+6}$ ---------------------(b) (Given)

⇒$13y + 78 = 24x+ 144$

⇒$13y-24x = 66$ -------------------(c)

Substitute the value of y from eq. (a) to eq. (c)

⇒$13(2x +2) - 24x = 66$

⇒$26x + 26 - 24x = 66$

⇒$2x = 40$

∴$x = 20$

Putting the value of x in eq. (a),

$y = 2(20) + 2 = 42$

Hence, the present ages of Sujatha and her mother are 20 years and 42 years respectively.

Answer 2

Given : present age of Sujatha's mother is two more than twice the age of Sujatha.

After 6 years , the ratio of the ages of the mother and Sujatha will be 24:13

To Find : their present ages​

Solution:

Let say Sujatha Present Age =  S years

Sujatha's mother is two more than twice the age of Sujatha.

Mother present age = 2S  + 2

After 6 years  Sujatha age =  S + 6 Years

After 6 years  Mothers age = 2S + 2 + 6 = 2S + 8 Years

ratio of the ages of the mother and Sujatha  24:13

=> (2S +  8)/(S + 6) = 24/13

=> (S + 4)/(S + 6)  = 12/13

=> 13S + 52 = 12S + 72

=> S = 20

Sujatha Present Age =  20  years

Mother present age = 2(20)  + 2 = 42 Years

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