The students of a class 10th have an average weight of 50 kg. The strength of the class is 49 students. On including the weight of the principal, the average weight shoots up by 0.8 kg. Find the weight of the principal?

Option b: 90. Solution: Step 1: Total weight of 49 students. Total49 = 49 × 50 = 2450 kg Step 2: New average after including principal. New avg = 50 + 0.8 = 50.8 kg New total (50 persons) = 50 × 50.8 = 2540 kg. Step 3: Weight of principal. Wprincipal = 2540 - 2450 = 90 kg Note: The computed weight is 90 kg (Option B), not 85 (Option C). Hence, Option B is the correct answer.

The students of a class $10^{th}$ have an average weight of $50$ kg. The strength of the class is $49$ students. On including the weight of the principal, the average weight shoots up by $0.8$ kg. Find the weight of the principal?

The correct answer is Option b: 90. **Step 1: Total weight of 49 students.** $$\text{Total}_{49} = 49 \times 50 = 2450 \text{ kg}$$ **Step 2: New average after including principal.** $$\text{New avg} = 50 + 0.8 = 50.8 \text{ kg}$$ New total (50 persons) $= 50 \times 50.8 = 2540$ kg. **Step 3: Weight of principal.** $$W_{principal} = 2540 - 2450 = 90 \text{ kg}$$ **Note:** The computed weight is **90 kg** (Option B), not 85 (Option C). Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 2023 Series IIQuestion 2916 of 473

All Questions

The students of a class $\displaystyle 10^{th}$ have an average weight of $\displaystyle 50$ kg. The strength of the class is $\displaystyle 49$ students. On including the weight of the principal, the average weight shoots up by $\displaystyle 0.8$ kg. Find the weight of the principal?

Options

A75

B90

C85

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 90

All Options:

A75
B90
C85
DNone of these

Detailed Solution & Explanation

**Step 1: Total weight of 49 students.**

\text{Total}_{49} = 49 \times 50 = 2450 \text{ kg}

**Step 2: New average after including principal.**

\text{New avg} = 50 + 0.8 = 50.8 \text{ kg}

New total (50 persons)

\displaystyle = 50 \times 50.8 = 2540

kg. **Step 3: Weight of principal.**

W_{principal} = 2540 - 2450 = 90 \text{ kg}

**Note:** The computed weight is **90 kg** (Option B), not 85 (Option C). Hence, **Option B** 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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