Question

In an objective type paper of $$150$$ questions:
John got $$80\mathrm{\%}$$ correct answers and Mohan got $$64\mathrm{\%}$$ correct answers.
What percent is Mohan’s correct answers to John’s correct answers?
A) $$100\mathrm{\%}$$
B) $$16\mathrm{\%}$$
C) $$64\mathrm{\%}$$
D) $$80\mathrm{\%}$$

Answer 1

Hint: This problem comes under topic percentage. First we need to convert percentage into fraction. Here we are given the correct answer percentage of John and Mohan and then with each of their marks again we find the percentage of Mohan correct answer to John correct answer and required formula and complete step by step explanation.

Formula used: ${\displaystyle \frac{\text{correct answer\% }}{100\mathrm{\%}}}\times \text{Total number of questions}$

Complete step-by-step answer:
John’s correct answer percentage $$=80\mathrm{\%}$$
We can find john’s marks for his correct answers using the formula mentioned in the formula used
$\Rightarrow {\displaystyle \frac{80}{100}}\times 150$
Dividing the terms we get,
$\Rightarrow 8\times 15=120$
Hence,
Marks for the correct answers of john $=120$
Mohan’s correct answer percentage $$=64\mathrm{\%}$$
We can find mohan’s marks for his correct answers using the formula mentioned in the formula used
$\Rightarrow {\displaystyle \frac{64}{100}}\times 150$
Multiply and divide the terms we get,
$\Rightarrow {\displaystyle \frac{64\times 15}{10}}$
Simplifying we get,
$\Rightarrow {\displaystyle \frac{960}{10}}=96$
Hence,
Marks for the correct answers of mohan $=96$
Now, we can find the % of Mohan’s correct answer to John’s correct answer by converting
Mohan’s correct answer to John’s correct answer fraction into percentage
$$\Rightarrow {\displaystyle \frac{\text{Mohan's correct answer mark}}{\text{John's correct answer mark}}}\times 100$$
$\Rightarrow {\displaystyle \frac{96}{120}}\times 100$
Simplifying we get,
$\Rightarrow {\displaystyle \frac{960}{12}}$
Hence we get,
$=80\mathrm{\%}$

$\therefore$ The percentage of Mohan’s correct answer to John’s correct answer is option (D) $80\mathrm{\%}$

Note: This kind of problem needs attention on percentage. The basic fraction into percentage conversion and fraction to percentage conversion has a huge role on it. We need to know to solve this kind of problem with their basic fraction multiplication and division. We need to obtain the equation and solve. To find the percentage from one to another and use the required formula. Fraction is quantity that represents a part of the whole. Suppose we say half of an apple. This half represents the fraction of the complete apple.