Question

What percent of $8.25m$ is $75cm$?
A. ${\displaystyle \frac{130}{11}}\mathrm{\%}$
B. ${\displaystyle \frac{75}{11}}\mathrm{\%}$
C. ${\displaystyle \frac{80}{11}}\mathrm{\%}$
D. ${\displaystyle \frac{100}{11}}\mathrm{\%}$

Answer 1

Hint: First of all we need to convert $8.25m$ into $cm$ or we can also convert $75cm$ into $m$ and then we will find the percentage of it. For example if we need the final percent of $x$ in $y$ then it will be given by ${\displaystyle \frac{x}{y}}\times 100$.

Complete step-by-step answer:
So as we are given two numbers $8.25m$ and $75cm$ and we need to find the percent of $75cm$ in $8.25m$. So first of all we need to convert the all units into a single unit for the ease to find out the percent.
So this can be done by the two cases so let us take them
Case 1
Here we need to convert $8.25m\text{ to cm}$ because here cm and m are both the units of length but during the measurement of the percentage we need to have the same units so that we can calculate the percentage.
So as we know that $1m=100cm$
So $8.25m=8.25(100)cm=825cm$
So $8.25m=825cm$
We need to find the percent of $75cm\text{ in 825}cm$
So the percent will be ${\displaystyle \frac{75}{825}}\times 100={\displaystyle \frac{100}{11}}\mathrm{\%}$
Case 2
Now we need to convert the $75cm\text{ to metre}$
As above we used the formula that $1m=100cm$ so we can also say that
$1cm={\displaystyle \frac{1}{100}}m$
So $75cm={\displaystyle \frac{75}{100}}m$
So now we can replace the $75cm\text{ into }{\displaystyle \frac{75}{100}}m$ and we can find the percentage as we have done earlier
So the percentage of ${\displaystyle \frac{75}{100}}m\text{ in 8}\text{.25}m$ which is
$={\displaystyle \frac{{\displaystyle \frac{75}{100}}}{8.25}}\times 100={\displaystyle \frac{7500}{825}}={\displaystyle \frac{100}{11}}\mathrm{\%}$
So from both the cases we get the same result which is ${\displaystyle \frac{100}{11}}\mathrm{\%}$
Hence option D is the correct one.

Note: We can do it in this way also
We can assume that $x\mathrm{\%}\text{ of 8}\text{.25}m\text{ is 75}cm$
So as we know that $1m=100cm$
$75cm=0.75m$
So we can write that
$8.25\times {\displaystyle \frac{x}{100}}=0.75$
$x={\displaystyle \frac{0.75}{8.25}}\times 100={\displaystyle \frac{100}{11}}\mathrm{\%}$