Question

In an objective type’s paper of \[150\] questions; John got \[80\% \] correct answers and Mohan got \[64\% \] correct answers. What percentage are Mohan’s correct answers to John's correct answers?
A. \[100\% \]
B. \[16\% \]
C. \[64\% \]
D. \[80\% \]

Answer 1

Hint: First we have to find marks on both Mohan and John, then we have to calculate percentage from Mohan’s to John.
Finally we get the required answer.

Formula used: Percentage \[{\text{ = }}\dfrac{{{\text{value}}}}{{{\text{Total value}}}}{{ \times 100}}\]
Value \[{\text{ = }}\dfrac{{{{Percentage \times Total value}}}}{{{\text{100}}}}\]
This formula helps to get the required result.

Complete step-by-step answer:
It is given that the total number of questions in an objective type paper which is \[150\]
Percentage of Mohan’s correct answers \[ = 64\% \]
Percentage of john’s correct answers \[ = 80\% \]
First, we have to find john’s marks,
Number of correct answers got by John is equal to \[{\text{ = }}\dfrac{{{{Percentage \times Total value}}}}{{{\text{100}}}}\]
Now substitute the values we get,
\[\dfrac{{80}}{{100}} \times 150 = 120\]
Hence, John got \[120\] marks
Next, we have to find Mohan’s marks,
Number of correct answers got by Mohan is equal to \[{\text{ = }}\dfrac{{{{Percentage \times Total value}}}}{{{\text{100}}}}\]
Now substitute the values we get,
\[\dfrac{{64}}{{100}} \times 150 = 96\]
Hence, Mohan got \[96\] marks
Now, we find Percentage of Mohan’s correct answers to John’s correct answers,
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 above formula.
\[\dfrac{{96}}{{120}} \times 100 = 80\% \]

So, the Percentage of Mohan’s correct answers to John’s correct answers is \[80\% \]

Note: In this question, we have alternative method as follows:
Total objective type question \[ = 150\]
Percentage of Mohan’s correct answers \[ = 64\% \]
Percentage of john’s correct answers \[ = 80\% \]
Now, we calculate the percentage of correct answers,
Percentage of correct answer from that of Mohan to John is,
Which can be done by,
\[\dfrac{{{\text{Mohan's percentage}}}}{{{\text{John's percentage}}}}{{ \times 100}}\]
Substitute the values we get,
\[\dfrac{{64}}{{80}} \times 100 = 80\% \]
\[\therefore \] The Percentage of Mohan’s correct answers to John’s correct answers is \[80\% \]