Question

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

Answer 1

Hint: We have to find the ratio of the two numbers . We solve this using the concept of solving the equations . We firstly consider the two numbers as two different variables and then put the values of the variables in the given condition as stated in the question and hence get the ratio of the two numbers .

Complete step-by-step answer:
When we are given a question such that given above then we solve the question considering each element whose value is to be calculated to be an unknown variable. Then we substitute the unknown variable in the conditions given in the question . Thereafter we solve the conditions using various solving methods such as the elimination method , substitution method , quadratic method etc .
Given : Let us consider that the first number is $x$ and the second number is $y$
Now , according to the question
\[y - \left( {\dfrac{{40}}{{100}}} \right) \times x = \left( {\dfrac{3}{5}} \right) \times y\]
On solving the equation , we get
\[y - \left( {\dfrac{2}{5}} \right) \times x = \left( {\dfrac{3}{5}} \right) \times y\]
Bringing terms of y on one side and x on the other side , we get
\[y - \left( {\dfrac{3}{5}} \right) \times y = \left( {\dfrac{2}{5}} \right) \times x\]
On simplifying , we get
\[\left( {\dfrac{2}{5}} \right) \times y = \left( {{\text{ }}\dfrac{2}{5}} \right) \times x\]
Cancelling the terms , we get
\[\left( {\dfrac{x}{y}} \right) = \left( {\dfrac{1}{1}} \right)\]
Thus the ratio of the first number to the second number is \[1:1.\]
So, the correct answer is “1:1”.

Note: We can also solve these types of questions using the quadratic formulas where the conditions give us the equation in the form of coefficients of ${x^2}$ .
The formula for solving the quadratic equation is as given below :
$x = \dfrac{{\sqrt {[ - b \pm [{b^2} - 4ac]]} }}{{2a}}$
Where $a$ is the coefficient of ${x^2},b$ is the coefficient of $x$ and $c$ is the coefficient of constant term where the equation is $a \times {x^2} + b \times x + c = 0$ .