There were 50 students in a class. 10 failed whose average marks were 2.5 . The total marks of class were 281 . Find the average marks of students who passed?

Option a: 6.4. Solution: Step 1: Find the sum of marks of failed students. Sum of failed = 10 × 2.5 = 25 Step 2: Find sum of marks of passed students. Passed students = 50 - 10 = 40 . Sum of passed = 281 - 25 = 256 Step 3: Average marks of passed students. Average of passed = 256/40 = 6.4 Note: The computed average is 6.4 (Option A), not 25 (Option B). Hence, Option A is the correct answer.

There were $50$ students in a class. $10$ failed whose average marks were $2.5$. The total marks of class were $281$. Find the average marks of students who passed?

The correct answer is Option a: $6.4$. **Step 1: Find the sum of marks of failed students.** $$\text{Sum of failed} = 10 \times 2.5 = 25$$ **Step 2: Find sum of marks of passed students.** Passed students $= 50 - 10 = 40$. $$\text{Sum of passed} = 281 - 25 = 256$$ **Step 3: Average marks of passed students.** $$\text{Average of passed} = \frac{256}{40} = 6.4$$ **Note:** The computed average is **6.4** (Option A), not 25 (Option B). Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 2929 of 473

All Questions

There were $\displaystyle 50$ students in a class. $\displaystyle 10$ failed whose average marks were $\displaystyle 2.5$ . The total marks of class were $\displaystyle 281$ . Find the average marks of students who passed?

Options

\displaystyle 6.4

\displaystyle 25

\displaystyle 256

\displaystyle 86

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Correct Answer

✅ Option a — $\displaystyle 6.4$

All Options:

A $\displaystyle 6.4$
B $\displaystyle 25$
C $\displaystyle 256$
D $\displaystyle 86$

Detailed Solution & Explanation

**Step 1: Find the sum of marks of failed students.**

\text{Sum of failed} = 10 \times 2.5 = 25

**Step 2: Find sum of marks of passed students.** Passed students

\displaystyle = 50 - 10 = 40

\text{Sum of passed} = 281 - 25 = 256

**Step 3: Average marks of passed students.**

\text{Average of passed} = \frac{256}{40} = 6.4

**Note:** The computed average is **6.4** (Option A), not 25 (Option B). Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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There were 50\displaystyle 5050 students in a class. 10\displaystyle 1010 failed whose average marks were 2.5\displaystyle 2.52.5. The total marks of class were 281\displaystyle 281281. Find the average marks of students who passed?