Question

A crew is made up of 8 men; the rest are women. $66\dfrac{2}{3}$ percent of the crew are men. How many people are there in the crew?

Answer 1

Hint: Now let us say there are x people in the group. Now we have $66\dfrac{2}{3}$ percent of the crew are men. Now the total number of men in the crew will be given by formula $\dfrac{\text{percentage of men}}{100}\times \text{total people}$ . Hence we will substitute the values in the formula and find the value of x. Hence we have the number of people in the group.

Complete step-by-step solution:
Now we are given the number of men in the group.
We know that percentage is nothing but the ratio per 100.
Hence when we have $66\dfrac{2}{3}$ percent of men we have per 100 people there are $66\dfrac{2}{3}$ men.
Hence percentage of men is given by $\dfrac{\text{number of men}}{\text{total people}}\text{ }\!\!\times\!\!\text{ 100}$
Hence number of men is given by $\dfrac{\text{percentage of men}}{100}\times \text{total people}$
Now let us say the total number of people in the crew is x.
Now we have $66\dfrac{2}{3}$ percent of the crew are men.
Hence we have the number of men in crew are $\dfrac{66\dfrac{2}{3}\times x}{100}$
Now let us first simplify the fraction.
We know that $a\dfrac{p}{q}=\dfrac{aq+p}{q}$ .
Hence using this we have, The number of men are $\dfrac{\dfrac{66\times 3+2}{3}\times x}{100}$ Now we are given that the total number of men in the crew are 8. Hence we get,
$\Rightarrow \dfrac{\dfrac{200x}{3}}{100}=8$
$\begin{align}
  & \Rightarrow \dfrac{200x}{300}=8 \\
 & \Rightarrow 2x=8\times 3 \\
\end{align}$
Now dividing the whole equation by 2 we get,
$\begin{align}
  & \Rightarrow x=4\times 3 \\
 & \Rightarrow x=12 \\
\end{align}$
Hence the total number of people in the crew is 12.

Note: Now note that since we have just men and women in the crew then the percentage of women in the crew will be $100-66\dfrac{2}{3}$ percent. Also since there are 12 people and 8 are men then the total number of women will be 4.