Question

the ages of vimla and sarita are in the ratio of 7:5 four years later their ages will be in the ratio 4:3 find their ages

Answer 1

Hope u like my process
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Let the age of vimla be x and sarita be y

So,

By problem
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$= > x : y = 7 : 5 \\ \\ = > x = \frac{7}{5} y........(1)$
Now,

After 4 years.,
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$= > (x + 4) : (y + 4) = 4 : 3 \\ \\ = > 3( \frac{7}{5} y + 4) = 4(y + 4) \\ \\ = > (21y + 60) \frac{1}{5} = 4y + 16 \\ \\ = > 21y + 60 = 20y + 8 0 \\ \\ = > 21y - 20y = 80 - 60 \\ \\ = > \bf \: y = \underline{20}$
So,
$= > \bf \: x = \frac{7}{5} \times 20 = 28$
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So,

Age of Vimla = 20 yrs

Age of sarita = 28 yrs.
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Hope this is ur required answer

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Answer 2

Ratio of their age = Vimla : Sarita = 7 : 5

Define their current age:

Let x be the constant ratio:

Vimla = 7x

Sarita = 5x

Define their age 4 years later:

Vimla = 7x + 4

Sarita = 5x + 4

Form equation and solve for x

4 years later, their ratio is : Vimla : Sarita = 4 : 3

3(7x + 4)= 4(5x + 4)

21x + 12 = 20x + 16

x = 4

Find their age:

Vimla = 7x = 7(4) = 28

Sarita = 5x = 5(4) = 20

Answer: Vimla is 28 and Sarita is 20