Question

The population of a village is 8000. Out of these, 80% are literate and of these literate people, 40% are women. Find the ratio of the number of literate women to the total population.

Answer 1

Hint: In this question, we need to determine the ratio of the number of literate women to the total population such that the population of a village is 8000 out of these, 80% are literate and of these literate people, 40% are women. For this, we will first calculate the total number of literate persons and then, the total number of the women who are literate. To get the result, we will divide the value of the literate women to the total population.

Complete step-by-step answer:
According to the question, the total population of literate people is 80% of the total population.
So, the population for the literate people is given as:
 $
\Rightarrow {P_L} = 80\% {\text{ of }}8000 \\
   = 6400 \;
  $
Also, it has been given that out of the literate population, 40% are women. So, the total population of literate women is calculated as:
 $
\Rightarrow {P_{WL}} = 40\% {\text{ of }}6400 \\
   = 2560 \;
  $
Now, according to the demand of the question, taking the ratio of the population of the literate women to the total population, we get
 $
\Rightarrow \dfrac{{{P_{WL}}}}{P} = \dfrac{{2560}}{{8000}} \\
   = \dfrac{8}{{25}} \;
  $
Hence, the ratio of the number of literate women to the total population is $ 8:25 $ .
So, the correct answer is “8:25”.

Note: In these types of questions, we always need to go through the language of the problem carefully as all the calculations depend on the words and the figures given in the question. Moreover, the concept of percentage to decimal conversion plays an important role here, so it is worth going to the conversion techniques as well.