Question

A candidate who gets 36% marks in the examination fails by 24 marks, but another candidate, who gets 43% marks, gets 18 more marks than the minimum pass marks. Find the maximum marks and percentage of pass marks? 

Answer 1

Hint: The only thing that you need to focus on to solve this problem is the percentage calculation. Take all the percentages to be with respect to the maximum marks. The two unknown elements are maximum marks and passing marks.

Complete step by step answer:

We are letting the maximum marks to be x and passing marks to be y.

Now, it is given in the question that if a student scores 36% in the exam fails by 24 marks. We can mathematically represent it as:

36% of x = y – 24

$\Rightarrow \dfrac{36}{100}\times x=y-24$ 

On taking 24 to the other side of the equation, we get

$\dfrac{36}{100}\times x+24=y...............(i)$

It is also given in the question that a candidate who gets 43% marks, gets 18 more marks than the minimum pass marks. When we write this in the form of a mathematical equation, we get

43% of x = y +18

$\Rightarrow \dfrac{43}{100}\times x=y+18$ 

Now, let us substitute the value of y from equation (i).

$\dfrac{43}{100}\times x=\dfrac{36}{100}\times x+24+18$

$\Rightarrow \dfrac{43}{100}\times x-\dfrac{36}{100}\times x=42$

$\Rightarrow \dfrac{7}{100}\times x=42$

$\Rightarrow x=\dfrac{42\times 100}{7}$

$\therefore x=600$

So, the maximum marks in the exam is 600 marks. On substituting the value of x in equation (i), we get

 $\dfrac{36}{1}\times 6+24=y$

$\Rightarrow 216+24=y$

So the passing marks = 240

Now, let us try to calculate the percentage passing marks.

Percentage of marks required for passing = $\dfrac{\text{passing marks}}{\text{Maximum marks}}=\dfrac{240}{600}\times 100 =40\%$

Therefore, the maximum marks is 600 marks, and the passing percentage is 40%.

Note: Always remember the percentages for an exam are calculated with respect to maximum marks. It is preferable to let the exact marks be variables; however, if you want, you can let the percentages as well.