Question

If $40$ percent of a number is subtracted from the second number then the second number is reduced to its $\frac{3}{5}$. Find the ratio between the first number and the second number.

Answer 1

Solve for the required ratio:

Given that if $40$ percent of a number is subtracted from the second number then the second number is reduced to its $\frac{3}{5}$

Let the first number be $x$ and the second number be $y$

As per the given condition the equation becomes

$\begin{array}{crcl}& y-40\%\left(x\right)& =& \frac{3}{5}y\\ \Rightarrow & \frac{40}{100}x& =& y-\frac{3}{5}y\\ \Rightarrow & \frac{2}{5}x& =& \frac{5-3}{5}y\\ \Rightarrow & \frac{2}{5}x& =& \frac{2}{5}y\\ \Rightarrow & x& =& y\\ \Rightarrow & \frac{x}{y}& =& 1\end{array}$

Hence the ratio between the first number and second number is $1:1$