Question

In a Maths Quiz of 60 questions, Chandra got $90\% $ correct answers and Ram got $80\% $ correct answers. How many correct answers did each give? What percent is Ram’s correct answer to Chandra’s correct answer?

Answer 1

Hint:Find the number of correct answers given by both Chandra and Ram by finding their percentage of correct answers of the total number of questions. That is,
= Percentage of correct answers$ \times $total number of questions.
After getting the number of correct answers of both Chandra and Ram, take the ratio of Ram’s correct answers to Chandra’s correct answer and multiply by 100 to get the required percentage.

Complete step-by-step answer:
It is given that there are 60 questions in the Maths Quiz, Chandra got $90\% $correct answers and Ram got $80\% $correct answers.
We have to find the number of correct answers given by both Chandra and Ram and then find the percent of Ram’s correct answer to Chandra’s correct answer.
As given that 90% of Chandra’s questions are correct, it means that we have to find 90% of 60 questions. Then, for Chandra,
Number of correct answers$ = 90\% {\text{ of }}60$
Number of correct answers$ = \dfrac{{90}}{{100}} \times 60$
Number of correct answers$ = 9 \times 6$
Number of correct answers$ = 54$
It means that Chandra corrected 54 answers out of 60 questions.
Now, we have given that Ram got $80\% $correct answers, it means that we have to find 80% of 60 questions. Then, for Ram,
Number of correct answers$ = 80\% {\text{ of }}60$
Number of correct answers$ = \dfrac{{80}}{{100}} \times 60$
Number of correct answers$ = 8 \times 6$
Number of correct answers$ = 48$
It means that Ram corrected 48 answers out of 60 questions.
Now, we have to find the percentage of Ram’s correct answer to Chandra’s correct answer.
We have calculated that Chandra corrected 54 answers out of 60 questions and Ram corrected 48 answers out of 60 questions. So, the percentage of Ram’s correct answer to Chandra’s correct answer is given as:
Percentage$\left( { = \dfrac{{48}}{{54}} \times 100} \right)\% $
Percentage$ = \dfrac{{800}}{9}\% $
Percentage$ = 88.89\% $
Therefore, the percentage of Ram’s correct answer to Chandra’s correct answer is $88.89\% $.

Note:
The percentage of Ram’s correct answer to Chandra’s correct answer defines how many times the number of the correct answer of Ram contains the number of correct answers of Chandra.