Measures of Central Tendency and DispersionMCQMTP June 2023 Series IIQuestion 2919 of 473
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The average salary of the whole employees in a company is 400\displaystyle 400 per day. The average salary of officers is 800\displaystyle 800 per day and that of clerks is 320\displaystyle 320 per day. If the number of officers is 40\displaystyle 40, then find the number of clerks in the company?

Options

A50
B100
C150
D200
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Correct Answer

✅ Option d — 200

All Options:

  • A50
  • B100
  • C150
  • D200

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Detailed Solution & Explanation

**Step 1: Set up the equation.** Let number of clerks =c\displaystyle = c. Number of officers =40\displaystyle = 40. 800×40+320×c40+c=400\frac{800 \times 40 + 320 \times c}{40 + c} = 400 **Step 2: Solve.** 32000+320c=400(40+c)32000 + 320c = 400(40 + c) 32000+320c=16000+400c32000 + 320c = 16000 + 400c 32000−16000=400c−320c32000 - 16000 = 400c - 320c 16000=80c16000 = 80c c=200c = 200 **Note:** The computed number of clerks is **200** (Option D), not 150 (Option C). Verification: (800×40+320×200)/(40+200)=(32000+64000)/240=96000/240=400\displaystyle (800 \times 40 + 320 \times 200)/(40+200) = (32000+64000)/240 = 96000/240 = 400 ✓ Hence, **Option D** 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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