Question

What number is $150\mathrm{\%}$ of $32$?

Answer 1

Hint: In this problem we need to find the $150\mathrm{\%}$ of $32$. For this we need to multiply $150\mathrm{\%}$ with a given number $32$. Now we will replace the percentage symbol with ${\displaystyle \frac{1}{100}}$. After that we will write all the numbers in the equation in factorization form. Now we will simplify the equation by cancelling all possible terms in the equation and performing some basic mathematical operation to get the required result.

Complete step by step answer:
Given number is $32$ and the given percentage is $150\mathrm{\%}$. The $150\mathrm{\%}$ of $32$ can be calculated by multiplying the both the values, then we will get
$150\mathrm{\%}\text{ of }32=150\mathrm{\%}\times 32$
Replacing percentage symbol$\left(\mathrm{\%}\right)$ with ${\displaystyle \frac{1}{100}}$ in the above equation, then we will get
$150\mathrm{\%}\text{ of }32=150\times {\displaystyle \frac{1}{100}}\times 32$
Writing $150$ as $15\times 10$, $100$ as $10\times 10$ in the above equation, then we will have
$150\mathrm{\%}\text{ of }32=15\times 10\times {\displaystyle \frac{1}{10\times 10}}\times 32$
Cancelling the $10$ which is in numerator and denominator, then we will get
$150\mathrm{\%}\text{ of }32=15\times {\displaystyle \frac{1}{10}}\times 32$
Writing $15$ as $3\times 5$, $10$ as $5\times 2$ and $32$ as $2\times 16$ in the above equation, then we will get
$150\mathrm{\%}\text{ of }32=3\times 5\times {\displaystyle \frac{1}{5\times 2}}\times 2\times 16$
Cancelling the terms $5$ and $2$ which are in numerator and denominator in the above equation, then we will have
$150\mathrm{\%}\text{ of }32=3\times 16$
We have the value $3\times 16$ as $48$. Substituting this value in the above equation, then we will get
$150\mathrm{\%}\text{ of }32=48$

Hence the $150\mathrm{\%}$ of $32$ is $48$.

Note: We can also solve this problem in another way. We can first calculate the value of $150\mathrm{\%}$ by multiplying the value with ${\displaystyle \frac{1}{100}}$. Then we will get ${\displaystyle \frac{150}{100}}$ on simplifying this value we will get ${\displaystyle \frac{3}{2}}$. Now multiplying this value with $32$, then we will get ${\displaystyle \frac{3}{2}}\times 32$. Simplifying this value, we will get $48$. From both the methods we got the same result.