A student's marks were incorrectly recorded as 45 instead of 6... | Mathematics MCQ | Examoogle

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A student's marks were incorrectly recorded as 45 instead of 63. Due to this, the average marks of the class increased by 0.6. What is the total number of students in the class?

Correct Answer

📐 MA • Math Direct FormulaMathematicsStatistics

Option B

Quick Summary:

Calculate the difference in marks ( $63 - 45 = 18$ ) and divide it directly by the increase in average ( $0.6$ ). This gives the total number of students immediately: $18 / 0.6 = 30$ .

📐MAMath SolutionDirect Formula

📋 Given

Incorrect marks = 45, Correct marks = 63, Increase in average marks = 0.6

🔢 Formula Used

N=Difference in SumChange in AverageN = \frac{\text{Difference in Sum}}{\text{Change in Average}}N=Change in AverageDifference in Sum​

⚡ Exam Hall Shortcut / Speed Trick

Calculate the difference in marks ( $63 - 45 = 18$ ) and divide it directly by the increase in average ( $0.6$ ). This gives the total number of students immediately: $18 / 0.6 = 30$ .

⚠️ Common Student Trap / Pitfall

Students often mistakenly subtract the average increase from the marks or try to find the total sum of the class, which is unnecessary and leads to calculation errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate the net change in total marks

The change in the total marks is the difference between the correct marks and the incorrectly recorded marks.

18=63−4518 = 63 - 4518=63−45

Define the relationship between total change and average change

Since the total increase in marks is distributed over $N$ students to increase the average by $0.6$ , we have $\text{Total Change} = N \times \text{Change in Average}$ .

18=N×0.618 = N \times 0.618=N×0.6

Solve for the number of students $N$

Rearranging the formula to find $N$ , we get $N = 18 / 0.6$ .

N=180.6=1806=30N = \frac{18}{0.6} = \frac{180}{6} = 30N=0.618​=6180​=30

✅

B is correct because the difference of 18 marks distributed over the class results in an increase of 0.6 per student, leading to a total of 30 students.

Core Concepts Used

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Arithmetic Mean Summation Properties Linear Equations

💡 EXAM TIP

This concept of 'Difference / Change' is widely applicable in speed, time, and distance problems, specifically when calculating distance given a change in speed.

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