The ratios of ages of A and B is $13:15$. After 9 years, the ratio will be $20:23$. What is the difference in years between ages?
Given: The ratios of ages of A and B is $13:15$. After 9 years, the ratio will be $20:23$.
To do: To find the difference in years between ages.
Solution:
$\because $ Ratio of ages of A and B $=13:15$
Let $13x$ and $15x$ are the ages of A and B respectively.
After $9$ years:
Age of A $=13x+9$
Age of B $=15x+9$
As given,
After $9$ years ratio of the ages of A and B is:
$( 13x+9):( 15x+9)=20:23$
$\Rightarrow \frac{13x+9}{15x+9}=\frac{20}{23}$
$\Rightarrow 23( 13x+9)=20( 15x+9)$
$\Rightarrow 299x+207=300x+180$
$\Rightarrow 300x-299x=207-180$
$\Rightarrow x=27$
$\therefore$ Age of A $=13x=13\times27=351$
Similarly Age of B $=15x=15\times27=405$
Difference between their ages $405-351=54$ years
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