Question

Convert each of the following pairs into percentages and find out which is more?
25 marks out of 30, 35 marks out of 40

Answer 1

Hint: In this question, we need to multiply each pair by 100 to convert into a percentage. To convert a fraction \[\dfrac{a}{b}\] into a percentage, we can multiply the fraction by 100 in the following manner:
$\dfrac{a}{b}\times 100=x\%$
Therefore, in this question, we shall follow a similar approach — first convert the fraction into percentage equivalent and then compare the two.

Complete step-by-step solution
The first fraction given to us is 25 marks out of 30, which can be written as \[\dfrac{25}{30}\]
To convert this fraction into a percentage, we shall multiply it by 100.
$\Rightarrow $ $\dfrac{25}{30}\times 100=83.33\%\quad \quad ...(1)$
The second fraction given to us is 35 marks out of 40, which can be written as \[\dfrac{35}{40}\]
To convert this fraction into a percentage, we shall again multiply it by 100.
$\Rightarrow $ $\dfrac{35}{40}\times 100=87.50\%\quad \quad ...(2)$
On comparing eq. (1) and eq. (2), it is clear that 87.50% is more than 83.33%. Therefore, we can conclude that 35 marks out of 40 are more than 25 marks out of 30.
This is the required solution.

Note:In the above question, if it had not been specified to use percentage as the method of comparison, we could have solved this question by finding the equivalent value of the fractions, which is given below:
$\dfrac{25}{30}=0.8333\quad \quad \quad ...(1)$
$\dfrac{35}{40}=0.8750\quad \quad \quad ...(2)$
From eq. (1) and eq. (2), $\dfrac{35}{40}$ is more.
This shows that even without the concept of percentage, we can compare two or more fractions.