A student's marks were incorrectly entered as 70 instead of 73... | Stage I (CBT I) MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

Stage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

A student's marks were incorrectly entered as 70 instead of 73. Due to this, the average marks of the class got decreased by $\frac{3}{2}$ . What is the number of students in the class?

A) $10$

B) $2$

C) $12$

D) $8$

Correct Answer

📚 GK • GK Direct FormulaStage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

Option B

$2$

Quick Summary:

Given: Actual mark = 73, Entered mark = 70, Decrease in average = 3/2 = 1.5

📐MAMath SolutionDirect Formula

📋 Given

Actual mark = 73, Entered mark = 70, Decrease in average = 3/2 = 1.5

🔢 Formula Used

Number of Students (N)=Difference in Total MarksChange in Average\text{Number of Students } (N) = \frac{\text{Difference in Total Marks}}{\text{Change in Average}}Number of Students (N)=Change in AverageDifference in Total Marks​

⚡ Exam Hall Shortcut / Speed Trick

Decrease in total marks = $73 - 70 = 3$ . Since each student's share of decrease is $\frac{3}{2}$ , total students $N = \frac{3}{3/2} = 2$ .

⚠️ Common Student Trap / Pitfall

Students often miscalculate the difference as $-3$ instead of $+3$ or divide the entered score by the average change directly.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate total difference in marks

Subtract the incorrectly entered mark from the correct mark to find the deficit in total marks.

Difference in total marks=73−70=3\text{Difference in total marks} = 73 - 70 = 3Difference in total marks=73−70=3

Set up the relation between average and total marks

Let $N$ be the total number of students in the class. The average marks decreased by $\frac{3}{2}$ . Therefore, the total decrease across all students equals $N \times \frac{3}{2}$ .

N×32=3N \times \frac{3}{2} = 3N×23​=3

Solve for N

Multiply both sides by $\frac{2}{3}$ to find the total number of students $N$ .

N=3×23=2N = 3 \times \frac{2}{3} = 2N=3×32​=2

✅

B is correct because solving the equation $N \times \frac{3}{2} = 3$ gives $N = 2$ students in the class.

Core Concepts Used

Click any tag to open in AI Tutor

Average Definition Data Correction in Averages Linear Equations in One Variable

💡 EXAM TIP

Questions involving incorrect entries in average calculations can always be solved directly using: $\text{Change in Average} = \frac{\text{Correct Value} - \text{Wrong Value}}{N}$ without calculating individual totals.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)