Question

If 75 percent of m is equal to k percent of 25, where k > 0, what is the value of m/k ?
A). \[\dfrac{3}{{16}}\]
B). \[\dfrac{1}{3}\]
C). \[\dfrac{3}{4}\]
D). \[3\]
E). \[\dfrac{{16}}{3}\]

Answer 1

Hint: The question is about the percentage which is a number of some sort of ratio i.e. express in terms of the fraction of the 100. Now if we have to solve the percent of any number that number is divided by the whole with multiply by 100 therefore the percentage is also known as the part per hundred or hundred part of one.

Complete step-by-step solution:
Step 1:
First we write the given data in terms of the equation.
 \[75\% \,of\,m = k\% \,of\,25\]
 \[\Rightarrow 75\% \, = \dfrac{{75}}{{100}},k\% \, = \dfrac{k}{{100}}\]
Now put the values
\[75\% \,\, \times m = k\% \, \times \,25\]
\[\Rightarrow \dfrac{{75}}{{100}}\,\, \times m = \dfrac{k}{{100}}\,\, \times \,25\]
Step 2:
Simplify this expression by using the cross multiplication and solve it. We got the desired ratio so
Now
\[\dfrac{{75}}{{100}}\,\, \times m = \dfrac{k}{{100}}\,\, \times \,25\]
 \[\Rightarrow \dfrac{{75m}}{{100}}\,\, = \dfrac{{\,25k}}{{100}}\,\,\]
\[\Rightarrow 75m = 25k\]
Now perform the cross multiplication so that we can take it as desired ratio and get result after simplifying the ratio so
\[\dfrac{m}{k} = \dfrac{{25}}{{75}}\]
\[\Rightarrow \dfrac{m}{k} = \dfrac{1}{3}\]
Hence we got the ratio of the m/k in terms of the rational numbers and it is matched with one of the given options provided by the question and the correct answer of the question is an option (b) satisfied.

Note: The good thing about percentage is that it can be solved easily. We have to just equal the percentage sign to the hundred part of one since the percentage is equal to the hundred part of one. And also we mentioned that the word percent can be divided like per plus cent or per hundred which is the same as we mentioned above.