Central Tendency & DispersionMTP June 2023 Series IQuestion 2914 of 473
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The mean annual salary of all employees in a company is 25,000\displaystyle 25,000. The mean salary of male and female employees is 27,000\displaystyle 27,000 and 17,000\displaystyle 17,000 respectively. Find the percentage of males and females employed by the company.

Options

A60%\displaystyle 60\% and 40%\displaystyle 40\%
B70%\displaystyle 70\% and 25%\displaystyle 25\%
C70%\displaystyle 70\% and 30%\displaystyle 30\%
D80%\displaystyle 80\% and 20%\displaystyle 20\%
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Correct Answer

✅ Option d — 80%\displaystyle 80\% and 20%\displaystyle 20\%

All Options:

  • A60%\displaystyle 60\% and 40%\displaystyle 40\%
  • B70%\displaystyle 70\% and 25%\displaystyle 25\%
  • C70%\displaystyle 70\% and 30%\displaystyle 30\%
  • D80%\displaystyle 80\% and 20%\displaystyle 20\%

Detailed Solution & Explanation

**Step 1: Let proportion of males =p\displaystyle = p and females =(1−p)\displaystyle = (1-p).** 27000p+17000(1−p)=2500027000p + 17000(1-p) = 25000 **Step 2: Solve.** 27000p+17000−17000p=2500027000p + 17000 - 17000p = 25000 10000p=800010000p = 8000 p=0.8=80%p = 0.8 = 80\% Females =1−0.8=0.2=20%\displaystyle = 1 - 0.8 = 0.2 = 20\%. **Note:** The computed percentages are **80% males and 20% females** (Option D). The `correct_option` is A (60% and 40%). Let us verify A: 27000×0.6+17000×0.4=16200+6800=23000≠25000\displaystyle 27000 \times 0.6 + 17000 \times 0.4 = 16200 + 6800 = 23000 \neq 25000. Verifying D: 27000×0.8+17000×0.2=21600+3400=25000\displaystyle 27000 \times 0.8 + 17000 \times 0.2 = 21600 + 3400 = 25000 ✓ Hence, **Option D** is the correct answer.

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