Question

In an objective type paper of 150 questions: John got 80% correct answer and Mohan got 64% correct answers.
(i) How many correct answers did each get? What percent is Mohan’s correct answer to John’s correct answer?

Answer 1

Hint: Use the formula to find the number of questions solved by each John and Mohan. Which is given below:
Number of questions solved $ = \dfrac{{{\text{percentage}}}}{{100}} \times 150$
This formula helps to get the required result

Complete step-by-step answer:
We have given the total numbers of questions in an objective type paper which is 150.
And the percentage of Mohan’s correct answer is given which is 64% and the percentage of John’s correct answer is 80%.
First, we will calculate the total number of correct answers scored by John and Mohan with the help of total number and their respective percentage.
So, the number of correct answers scored by John is equal to $ = \dfrac{{{\text{percentage}}}}{{100}} \times 150$(total questions).
Now, substitute the value of percentage in the above formula.
$
   = \dfrac{{80}}{{100}} \times 150 \\
   = 120 \\
$
This means there are $120$ correct answers scored by John out of $150$ questions..
Now, we will calculate the number of correct answers scored by Mohan it is equal to.
$
   = \dfrac{{64}}{{100}} \times 150 \\
   = 96 \\
$
This means there are $96$ correct answers scored by Mohan out of $150$ questions.
Now, we will calculate the percentage of Mohan’s correct answers to John’s correct answer.
Which can be done by $\dfrac{{{\text{Mohan's correct answer}}}}{{{\text{John's correct answer}}}} \times 100$
Now, substitute the obtained values of Mohan’s correct answer and John’s correct answer in the above formula.
$
   = \dfrac{{96}}{{120}} \times 100 \\
   = 80\% \\
$

So, the percentage of Mohan’s correct answer to John’s correct answer is $80\% $.

Note: We have given that John gets $80\% $ of correct answers, it means that his $20\% $questions are wrong, then find the $20\% $ of 150 which given the number of wrong questions.
$20\% {\text{ of }}150$
$ \Rightarrow \dfrac{{20}}{{100}} \times 150 = 30$
It means that $30$ questions out of $150$questions are wrong, then the number of correct answers are:
Correct answers $ = 150 - 30$
Number of correct answer $ = 120$
So, John’s correct answers are 120 out of 150 questions.