Question

In an examination, first division marks are 60%. A student secures 538 marks and misses the first division by 22 marks. Find the total marks of the examination.

Answer 1

Hint: We will first add 22 to 538 marks to make it exactly 60% of the total marks for the examination. Now, assume the total marks to be Rs. X and then put in its 60% to be equal to 538 + 22 and thus we have the value of x.

Complete step-by-step answer:
Since, we are already given that the students secured 538 marks and still he missed the first division cut – off by 22 marks to reach the benchmark of 60%.
So, if we add 22 to 538, we will get exactly 60% of the marks.
Therefore, the 60% of the total marks is 538 + 22 = 560 marks.
$\therefore $ 60% of the total marks is 560 marks.
Let the total marks of the examination be x.
So, we will have that 60% of x will be 560.
$ \Rightarrow \dfrac{{60}}{{100}}x = 560$
Cross multiplying it to get the following expression:-
$ \Rightarrow 60x = 560 \times 100$
Simplifying the RHS of the above expression to get the following expression:-
$ \Rightarrow 60x = 56000$
Taking the 60 from multiplication in LHS to division in RHS to get the following expression:-
$ \Rightarrow x = \dfrac{{56000}}{{60}}$
Simplifying it further to get:-
$ \Rightarrow x = \dfrac{{2800}}{3} = 933.\bar 3$

$\therefore $ The total marks of the examination is $933.\bar 3$.

Note: The students must note that we have used the concept of changing percent to fraction here. If you need to convert any fraction to percent, just multiply it by 100 and if you need to convert percentage into fraction, then divide the percentage by 100 to get it. Here, we did use that concept only.
Also note that the word ‘of’ generally means multiplication. Like here we had 60% of total marks as the first division cut – off.
Percent and percentage mean the same things almost. There is a slight difference between both. For example:- 20% of 5 pens is 1 pen and 1 pen is the percentage. But we use them as similar in the questions.