Question

A number, when 35 is subtracted from it, reduces to its 80 percent. What is the four fifth of that number?

Answer 1

To solve this problem first we will assume the number to be equal to some variable say X then we will subtract 35 from the number X and equate it with the 80% of the X. from the obtained equation we will find out the value of X and after that we will multiply it by $\dfrac{4}{5}$ which will give us the required answer.

Complete step-by-step answer :
We are given a number such that when 35 is subtracted from it, it reduces to its 80 percent.
So to solve this we will assume the number to be X
So when 35 is subtracted it will be like this,
X – 35 $....\left( 1 \right)$
And 80 percent of the number X will be given as,
$\begin{aligned} & \dfrac{80}{100}\times X \\\ & \dfrac{4}{5}X\,\,...\left( 2 \right) \\\ \end{aligned}$
Now according to the question equation (1) and (2) are equal so equation both we get
$\begin{aligned} & X-35=\dfrac{4}{5}X \\\ & X-\dfrac{4}{5}X=35 \\\ & \dfrac{X}{5}=35 \\\ & X=175 \\\ \end{aligned}$
Hence we get the number as 175
Now we have to find the four fifth of the number so for that we will have to multiply the number with $\dfrac{4}{5}$, hence we get
$\begin{aligned} & \dfrac{4}{5}X \\\ & =\dfrac{4}{5}\times 175 \\\ & =4\times 35 \\\ & =140 \\\ \end{aligned}$
Hence we get our required answer as 140.

Note : Whenever questions related to statements are given try to change the statements into the equations to solve it otherwise most of the students miss out one or the other case and end up with the wrong answer. And also to solve this question you need to have the prior knowledge of how to calculate percentages otherwise you would not be able to calculate 80% of the given number and hence cannot solve it.