Question

In an examination Ramesh secured 574 marks and Rekha secured $76\% $of the total marks. If Ramesh secured $82\% $ of the total marks’ the difference in their marks is _____.

Answer 1

Hint:
In this problem first, we calculate the total marks with the help of given percentage and marks by using the formula of percentage, which is given by the formula $\dfrac{{{\text{marks}}\,{\text{secured}}}}{{{\text{total}}\,{\text{marks}}}} \times 100$.
Complete step-by-step answer:
Given: Ramesh secured $ = $ 574 marks
Rekha secured $ = $ 76 percent marks
Ramesh secured $ = $ 82 percent marks
Let the total marks in the examination is $x$.
So, now we will compute total marks or we can say that we will find the value of x from Ramesh score.
We know that, percentage of marks is given by the formula $\dfrac{{{\text{marks}}\,{\text{secured}}}}{{{\text{total}}\,{\text{marks}}}} \times 100$
Mathematically, isolate the formula for total marks, that is,
Total marks $ = \dfrac{{{\text{marks}}\,{\text{secured}}}}{{{\text{percentage}}\,{\text{of}}\,{\text{marks}}}} \times 100$

For Ramesh:
Substitute 579 for marks secured, 82 for percentage of marks and $x$ for total marks in the above formula:
$x = \dfrac{{579}}{{82}} \times 100$
Mathematically, compute the value of $x$.
$x = 700$
It means total marks is 700.
Now we will find the total marks of Rekha from their percentage
For Rekha:
Marks $ = \dfrac{{{\text{percentage marks}}}}{{{\text{100}}}}{\text{ \times total}}$
Substitute 76 for percentage marks and 700 for total marks to find the secured marks by Rekha,
Rekha’s marks $ = \dfrac{{76}}{{100}} \times 700$
For Rekha’s marks simplify the obtained values,$ = $ 532
Now, we will find the difference of marks between them by subtracting the marks obtained by Rekha from the marks obtained by Ramesh.
Difference $ = $ Ramesh’s marks $ - $ Rekha’s marks
Put all the value, we get
Difference between marks $ = 574 - 532$
$ = 42$
Note:
Differences of marks can be found only if we know the secured marks of Ramesh and Rekha and Rekha’s marks can be obtained by using total marks, so find total marks first.