Question

Raja got 76% marks and Seema got 480 marks in a test. The maximum marks of the test is equal to the marks obtained by Raja and Seema together. How many marks did Raja score in the test?

Answer 1

Hint: In the above we need to determine the total score of raja but before that we must have the information of the maximum marks that means first we will be determining the total marks of the and after the determination of the total marks we can determine the score of raja from the maximum marks

Complete step-by-step answer:
Let us consider that the total marks raja score be y out of the maximum marks be x then in such case we can use the formula of percentage
So, we can say that
$Percentage = \dfrac{\text{Marks obtained}}{\text{total marks}} \times 100$
Now, substituting the required condition which we have considered in beginning
$76 = \dfrac{y}{x} \times 100$
So, let us determine the value of y which is the total marks obtained then on such case
$y = \dfrac{{76x}}{{100}}$
Hence, the above represent the score of raja out of the total marks x
Now,
It is given that if we add the total score of both raja and seema then we get the total marks from which they have scored
Total score of seema is $480$ then in such case we can form the equation as follows
$x = 480 + y$
In the above equation x represent the value of total marks while y represents the value of score of raja
Which we have determined above
Hence, the above equation can be simplified can follows
$x = 480 + \dfrac{{76x}}{{100}}$
 On simplifying the above
$x100 = 48000 + 76x$
On simplifying for the value of x, we get
$100x - 76x = 48000$
Hence, we get
$24x = 48000$
Then the value of x or the maximum marks is
$x = 2000$
Now, we need to determine the total marks of raja
$x = 480 + y$
Now, substituting the value of x, we get
$2000 = 480 + y$
Simplifying , we get
$2000 - 480 = y$
$y = 1520$

So, the total score of raja is 1520 marks

Note: Since it is given that the total score of raja and seema is equal to the total marks hence it becomes easy to determine the result for the score of raja but we can also use the formula for the percentage to determine the score of raja as we know the value of percentage and total marks.