Question

Ratio of age of Ram and his father is3:5 before ten years ,after ten years their age ratio becomes 7:11 then find their present age​

Answer 1

Let the present age of Ram and his father be x and y.

A.t.q,

$\mathtt{Before \; ten \; years } \\ \\ \Rightarrow \qquad \frac{x-10}{y-10} = \frac{3}{5} \\ \\ \Rightarrow \qquad 5(x-10) = 3(y-10) \\ \\ \Rightarrow \qquad 5x - 50 = 3y - 30 \\ \\ \Rightarrow \qquad 5x - 3y = 20 \qquad \qquad (1) \\ \\ \mathtt{After \; ten \; years } \\ \Rightarrow \qquad \frac{x+10}{y+10} = \frac{7}{11} \\ \\ \Rightarrow \qquad 11(x+10) = 7(y+10) \\ \\ \Rightarrow \qquad 11x + 110 = 7y + 70 \\ \\ \Rightarrow \qquad 11x - 7y = -40 \qquad \qquad (2) \\ \\ \mathtt{Multiplying \: (1) \: by \: 7 \: and \: (2) \: by \: 3} \\ \\ 35x - 21y = 140 \\ 33x - 21y = -120 \\ \boxed{2x = 260} \\ \bold{Therefore} \; x = 130 \\ \\ \mathtt{Putting \: \boxed{x=130} \: in \: (1) , \: we\: get\: y } \\ \Rightarrow \qquad 5x - 3y = 20 \\ \Rightarrow \qquad 5(130) - 3y = 20 \\ \Rightarrow \qquad -3y = 20 - 650 \\ \boxed{y = 210} \\ \\ \bold{Ram's \: age \: is \: 130 \: years \: and \: his \: father's\: age \: is \: 210 \: years }$