Question

Of the 1000 persons of a town, \[60\% \] are males of whom, \[20\% \] are literate. If all the persons \[25\% \] are literate then what percentage of the females of the town are literate?
A) \[32.5\% \]
B) \[22.5\% \]
C) \[45\% \]
D) \[13\% \]

Answer 1

Hint:
Here, I will use the given information and find the number of males as well as the total number of females in the town. We will subtract the number of literate males from the total literate people to get the number of literate females. We will then divide the number of literate females by the total females and then multiply it by 100 to get the required percentage.

Complete Step by Step Solution:
Total number of persons in a town is 1000 out of which there are \[60\% \] of males. So,
Total number of males \[ = 60\% \] of 1000
\[ \Rightarrow \] Total number of males \[ = \dfrac{{60}}{{100}} \times 1000 = 600\]
Now to find the total number of females we will subtract the number of males from the total number of persons in a town. Therefore, we get
Total number of females \[ = \left( {1000 - 600} \right) = 400\]
Now, it is given that of the total people, \[25\% \] are literate. So,
The total literate people \[ = 25\% \] of 1000
\[ \Rightarrow \] The total literate people \[ = \dfrac{{25}}{{100}} \times 1000 = 250\]
Also, \[20\% \] of males are literate.
The total literate males \[ = 20\% \] of 600
\[ \Rightarrow \] The total literate males \[ = \dfrac{{20}}{{100}} \times 600 = 120\]
Therefore, if there are 250 literate people and 120 among them are males.
Then, the total number of females who are literate \[ = \left( {250 - 120} \right) = 130\]
Now, we have to find the percentage of the females of the town who are literate.
Here, the number of females is 400.
And, the number of females who are literate among them are 130.
Therefore
 The percentage of the females of the town who are literate \[ = \dfrac{{130}}{{400}} \times 100\]
Multiplying the terms, we get
 \[ \Rightarrow \] The percentage of the females of the town who are literate \[ = \dfrac{{130}}{4} = 32.5\% \]
Therefore this is the required answer.

Hence, option A is the correct answer.

Note:
Percentage is a ratio or a number that is expressed as a fraction of 100 and is denoted by \[\% \] sign. In order to express two numbers, say \[A\] as a percentage of \[B\]. Then the required percentage will be of the form: \[\dfrac{A}{B} \times 100\].
In this question, we were asked to find the percentage of females of the town who are literate; hence, we divided the literate females by the total females and then multiplied it by 100. But, if we would have divided the literate females by let’s say, the total number of people in the town or the total number of literate people in the town, then our percentage will be wrong.