The ages of Nitish and Vinnee are in the ratio 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages now ?

13 Years
25 Years
37 Years
49 Years

Answer:- 1

Explanation:-

Solution:

Let Nishi's age be 6x years,
Then Vinnee's age = 5x years

\begin{aligned} ∴ \frac{6 x + 9}{5 x + 9} = \frac{9}{8} \\ \Rightarrow 8 (6 x + 9) = 9 (5 x + 9) \\ \Rightarrow 48 x - 45 x = 81 - 72 \\ \Rightarrow 3 x = 9 \\ \Rightarrow x = 3 \\ Difference in their ages \\ = (6 x - 5 x) \\ = x, years \\ = 3 years \end{aligned}

$\eqalign{ & \therefore \frac{{6x + 9}}{{5x + 9}} = \frac{9}{8} \cr & \Rightarrow 8\left( {6x + 9} \right) = 9\left( {5x + 9} \right) \cr & \Rightarrow 48x - 45x = 81 - 72 \cr & \Rightarrow 3x = 9 \cr & \Rightarrow x = 3 \cr & {\text{Difference in their ages}} \cr & {\text{ = }}\left( {6x - 5x} \right) \cr & = x,{\text{years}} \cr & = {\text{3 years}} \cr}$