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A maths exam is marked out of 120. Passing mark is 40 %. What are the marks required for passing?
(a). 48
(b). 110
(c). 54
(d). 72

Last updated date: 16th May 2024
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Hint: Recall the formula for percentage, that is, Percentage = \[\dfrac{{{\text{Required value}}}}{{{\text{Total value}}}} \times 100\% \]. Use this formula to calculate the marks required for passing the exam.

Complete step-by-step answer:
Percentage of a quantity means a fraction of the quantity expressed by taking a hundred as a whole. 100 % means the entire quantity or the whole. The word percent comes from Latin word Per Cent where Centum means hundred.
Percentage is just a convenient way to express a fraction with hundred as a whole.
Percentage is a number expressed as a fraction of 100. It is calculated by multiplying the numeric of the ratio by 100.
When we need to find the percentage of students passed the exam, we find the ratio of the number of students passed the exam to the number of students who attended the exam and multiply the ratio by 100.
Hence, in the given question, the total marks are 120 and to pass the exam, a student must score at least 40 %. We know that percent of pass marks is equal to the ratio of the number of pass marks to the total number of marks multiplied by 100.
Let the number of pass marks required be x. Then, we have the following:
Percentage = \[\dfrac{{{\text{Pass Marks}}}}{{{\text{Total Marks}}}} \times 100\% \]
The total marks are 120.
\[40\% = \dfrac{x}{{120}} \times 100\% \]
Solving for x, we get:
\[x = \dfrac{{40}}{{100}} \times 120\]
\[x = 4 \times 12\]
\[x = 48\]
Hence, 48 marks are required for passing.

Note: Percent is out of 100 and the total marks is 120. Hence, if the passing percentage is 40, the passing marks will not be 40 but slightly higher than that.