Question

Find the value of $x$ if $x - 30\% $of $x = 35$.

Answer 1

Hint: To convert a percent number into fraction we will divide it by 100 e.g. $a\% = \dfrac{a}{{100}}$. To find the value of $x$ from the given equation $x - 30\% $of $x = 35$, first convert the $30\% $ into fractions. After that the $30\% $ of $x$ means $30\% $ is multiplied by $x$. Now, by putting their value in the given equation we can find the value of $x$.

Complete step-by-step answer:
First of all, what is given to us? We have given with an equation i.e.
$ \Rightarrow x - 30\% $of $x = 35$ ………….(1)
Now, see what we have to find? We have to find the value of $x$.
Firstly, convert the $30\% $ into fractions by dividing 30 with 100, we get,
$ \Rightarrow 30\% = \dfrac{{30}}{{100}}$
Now, reduce this fraction into simplest form by cancelling one zero from numerator and denominator we get,
$ \Rightarrow 30\% = \dfrac{3}{{10}}$
Now, what is $30\% $ of $x$. In this ‘of’ means multiply i.e. that fraction of $x$ is taken. So, it is given as:
$ \Rightarrow 30\% \times x = \dfrac{3}{{10}} \times x = \dfrac{3}{{10}}x$ …………(2)
From (1) and (2), we get,
$ \Rightarrow x - \dfrac{3}{{10}}x = 35$
Taking L.C.M from L.H.S we get,
$ \Rightarrow \dfrac{{10 - 3}}{{10}}x = 35$
By subtracting the numbers in numerator of L.H.S we get,
$ \Rightarrow \dfrac{7}{{10}}x = 35$
Taking 10 from denominator of L.H.S in numerator of R.H.S, we get,
$ \Rightarrow 7x = 35 \times 10$
Taking 7 to other side we get,
$ \Rightarrow x = \dfrac{{35 \times 10}}{7}$
By solving this we get,
$ \Rightarrow x = 50$
Hence, the value of x is 50.

Note: Don’t forget to convert 30 percent into fraction, students can make this type of mistake. It is noted that if options are given to us then we simply put the values of the option in the equation and we can find the value of x in a simple way.
Alternate way to solve this question is if we subtract a number from its some percentage of number i.e. $x - a\% \times x$ then the result obtained is $100\% - 30\% = 70\% $ of that number. So, we can do this in mind and in objective type questions it can save our time. Also, we can directly divide 35 with 7 and we get 5. Finally, you multiply it by 10 and 50 is obtained. This all can be also solved in the thought process to save time.