Math Problem Statement

A student scored 45% in an exam and failed by 15 marks. If the passing marks are 150, what were the total marks for the exam?

Solution

Let's denote the total marks for the exam as TT.

The student scored 45% of the total marks, which can be expressed as:

Marks obtained by the student=0.45T\text{Marks obtained by the student} = 0.45T

It is given that the student failed by 15 marks, which means that the marks obtained by the student were 15 marks less than the passing marks of 150. Therefore, we can write:

0.45T=150150.45T = 150 - 15

Simplifying the equation:

0.45T=1350.45T = 135

Now, solving for TT:

T=1350.45=300T = \frac{135}{0.45} = 300

So, the total marks for the exam were 300.

Would you like any further details or have any other questions?


Here are some related questions:

  1. If a student scored 60% in the same exam, how many marks did they obtain?
  2. What percentage would a student need to pass if the total marks were 400?
  3. If another student scored 75% in this exam, how many marks did they score above the passing mark?
  4. What is the minimum percentage required to pass the exam?
  5. If the exam were out of 500 marks, what would be the new passing mark if the percentage required to pass remains the same?
  6. How many marks would a student lose if they scored 10% less than the passing percentage?
  7. What would be the difference in marks between a student who scored 85% and the student who scored 45%?
  8. How many marks would a student score if they obtained 90% in the exam?

Tip: When dealing with percentage problems, it's often useful to express all values in terms of the unknown variable before solving for it.

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Math Problem Analysis

Mathematical Concepts

Percentage
Equations

Formulas

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Theorems

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Suitable Grade Level

High School