Question

In a village, \[\dfrac{3}{{28}}\]of the people are college graduates, \[\dfrac{3}{{14}}\]of them are school graduates and \[\dfrac{4}{7}\]of them have completed their primary education. Which group of people is the largest and which is the least?

Answer 1

Hint: First assume the total number of the village as x and then use the given fractions to define the part of peoples according to their educations and then make the denominator same so that we approach the required result.

Complete step by step solution:
We have given that \[\dfrac{3}{{28}}\]of the people are college graduates, \[\dfrac{3}{{14}}\]of them are school graduates and \[\dfrac{4}{7}\]of them have completed their primary education.
We have to find, which group of people is the largest and which is the least.
Part of people who are college graduates\[ = \dfrac{3}{{28}}\]
Part of people who are school graduates\[ = \dfrac{3}{{14}}\]
Part of people who have completed their primary education\[ = \dfrac{4}{7}\]
Assume that the total number of people in the village be$x$, then the rest people of the village are given as:
$\dfrac{3}{{28}} + \dfrac{3}{{14}} + \dfrac{4}{7} + {\text{rest people}} = 1$
$ \Rightarrow {\text{Rest people}} = 1 - \left( {\dfrac{3}{{28}} + \dfrac{3}{{14}} + \dfrac{4}{7}} \right)$
$ \Rightarrow {\text{Rest people}} = 1 - \left( {\dfrac{{25}}{{28}}} \right) = \dfrac{3}{{28}}$
Now, to find the largest and least among them we will make their denominators same as follows:
College graduates peoples\[ = \dfrac{3}{{28}}x\]
School Graduates people\[ = \dfrac{{3 \times 2}}{{14 \times 2}}x = \dfrac{6}{{28}}x\]
Primary Education\[ = \dfrac{{4 \times 4}}{{7 \times 4}}x = \dfrac{{16}}{{28}}x\]
Rest peoples of the village$ = \dfrac{3}{{28}}x$
Now, we can see the largest value of the numerator is $16$ and the least value at the denominator is $3$.

$\therefore$The group of Primary Education is the largest and least is one is of College Graduates.

Note:
For making the denominator of all the fraction the same, we need to find the least common multiple of the denominators, and then multiply the numerator and the denominator so, that their denominators equal to the LCM.