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If $\frac{4}{5}$ of a number exceeds its $\frac{3}{7}$ by $65$, then find the number.
Given: $\frac{4}{5}$ of a number exceeds its $\frac{3}{7}$ by $65$.
To do: To find the number.
Solution:
Let the number is $x$.
Then, according to the given question,
$x\times \frac{4}{5}=x\times \frac{3}{7}+65$
$\Rightarrow \frac{4x}{5}-\frac{3x}{7}=65$
$\Rightarrow \frac{( 28x-15x)}{35}=65$
$\Rightarrow 13x=65\times 35$
$\Rightarrow x=\frac{( 65\times 35)}{13}$
$\Rightarrow x=5\times 35$
$\Rightarrow x=175$
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