Answer
Verified
412.5k+ views
Hint: The only thing that we 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 20% in the exam fails by 5 marks. We can mathematically represent it as:
20% of x = y – 5
$\Rightarrow \dfrac{20}{100}\times x=y-5$
On taking 5 to the other side of the equation, we get
$\dfrac{20}{100}\times x+5=y...............(i)$
It is also given in the question that a candidate who gets 30% marks, gets 20 more marks than the minimum pass marks. When we write this in the form of a mathematical equation, we get
30% of x = y +20
$\Rightarrow \dfrac{30}{100}\times x=y+20$
Now, let us substitute the value of y from equation (i).
$\dfrac{30}{100}\times x=\dfrac{20}{100}\times x+20+5$
$\Rightarrow \dfrac{30}{100}\times x-\dfrac{20}{100}\times x=25$
$\Rightarrow \dfrac{10}{100}\times x=25$
$\Rightarrow x=\dfrac{25\times 100}{10}$
$\therefore x=250$
So, the maximum marks in the exam is 250 marks. On substituting the value of x in equation (i), we get
$\dfrac{20}{100}\times 250+5=y$
$\Rightarrow 50+5=y$
$\therefore y=55$
Now, let us try to calculate the percentage passing marks.
Percentage of marks required for passing = $\dfrac{\text{passing marks}}{\text{Maximum marks}}\times 100=\dfrac{y}{x}\times 100=\dfrac{55}{250}\times 100=22%$
Therefore, the maximum marks is 250 marks, and the passing percentage is 22%.
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 we want, we can let the percentages as well.
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 20% in the exam fails by 5 marks. We can mathematically represent it as:
20% of x = y – 5
$\Rightarrow \dfrac{20}{100}\times x=y-5$
On taking 5 to the other side of the equation, we get
$\dfrac{20}{100}\times x+5=y...............(i)$
It is also given in the question that a candidate who gets 30% marks, gets 20 more marks than the minimum pass marks. When we write this in the form of a mathematical equation, we get
30% of x = y +20
$\Rightarrow \dfrac{30}{100}\times x=y+20$
Now, let us substitute the value of y from equation (i).
$\dfrac{30}{100}\times x=\dfrac{20}{100}\times x+20+5$
$\Rightarrow \dfrac{30}{100}\times x-\dfrac{20}{100}\times x=25$
$\Rightarrow \dfrac{10}{100}\times x=25$
$\Rightarrow x=\dfrac{25\times 100}{10}$
$\therefore x=250$
So, the maximum marks in the exam is 250 marks. On substituting the value of x in equation (i), we get
$\dfrac{20}{100}\times 250+5=y$
$\Rightarrow 50+5=y$
$\therefore y=55$
Now, let us try to calculate the percentage passing marks.
Percentage of marks required for passing = $\dfrac{\text{passing marks}}{\text{Maximum marks}}\times 100=\dfrac{y}{x}\times 100=\dfrac{55}{250}\times 100=22%$
Therefore, the maximum marks is 250 marks, and the passing percentage is 22%.
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 we want, we can let the percentages as well.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE