Two numbers are in ratio 5:6 …
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Sia ? 6 years, 6 months ago
Let the two numbers be x and y.
Then, by first Condition, ratio of these two numbers = 5:6.
x : y = 5 : 6
{tex}\Rightarrow\;\;\frac xy=\;\frac56{/tex}
{tex}\Rightarrow\;\; y=\;\frac{6x}5{/tex} ............ (i)
As per second condition if 8 is subtracted from each of the numbers, then ratio becomes 4:5.
{tex}\Rightarrow\;\;\frac{x-8}{y-8}=\;\frac45{/tex}
5x - 40 = 4y - 32
5x - 4y = 8 ........... (ii)
Now Put the value of y from (i) to (ii), we get
{tex}5x-4\left(\frac{6x}5\right)=\;8{/tex}
⇒ 25x - 24x = 40
⇒ x = 40
Put the value of x in equation (i), we get
{tex}\begin{array}{l}y=\;\frac65\times40\\=6\times\;8\\=\;48\end{array}{/tex}
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