Question

The ratio of the ages of ajay and vijay is 3:4.After 5 years the new ratio of their ages will be 4:5.Find out the present age (in years) of vijay?

Answer 1

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Let the age of Ajay and Vijay is 3x and 4x

After 5 years their age are 3x+5 and 4x+5

ATQ

$\frac{3x + 5}{4x + 5} = \frac{4}{5} \\ 5(3x + 5) = 4(4x + 5) \\ 15x + 25 = 16x + 20 \\ 16x - 15x = 25 - 20 \\ x = 5 \\ so \: \: ajay \: age \: is \: 3 \times 5 = 15years \\ and \: vijay \: age \: is \: 4 \times 5 = 20years$

Hope it helps you

Answer 2

Present age of Vijay (in years) is

Let

   Present age of Ajay = x

   Present age of Vijay = y

         Ratio = 3:4

      ⇒ $\frac{x}{y} = \frac{3}{4}$

      ⇒ 4x = 3y

      ⇒ 4x - 3y = 0 -------------------------------(1)

    Ratio after 5 years = 4:5

     ⇒ $\frac{x+5}{y+5} = \frac{4}{5}$

     ⇒ 5x + 25 = 4y + 20

     ⇒ 5x - 4y + 5 = 0 ---------------------------(2)

Solving (1) and (2), we get    (please kindly refer attachment for solving steps)

     x = 15 years  ,     y = 20 years

∴ Age of Vijay = 20 years