Question

Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is $3:5$. After Nora gives Rs. $150$ to Kate, the ratio of the amount of money Kate has to that of Nora becomes $7:9$. Find the sum of money Kate had initially.

Answer 1

Let Kate has $x$

and Nora has $y$ sum of money

Now, According to Question

$\frac{3}{5}=\frac{x}{y}\Rightarrow y=\frac{5}{3}x$

After Nora gives Kate Rs.$150$

$\frac{7}{9}=\frac{x+150}{y-150}\Rightarrow 7y-1050=9x+1350\Rightarrow 7y-9x=2400\Rightarrow 7\times \frac{5}{3}x-9x=2400\Rightarrow x=900$

So, Kate had Rs.$900$ initially