Central Tendency & DispersionMTP Nov 18Question 2880 of 473
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The mean age of a group of 100 men and women is 25 years. If the mean age of the group of men is 26, then that of the group of women is 21 then the ratio of women and men in the group:

Options

A1:1
B1:2
C1:3
D1:4
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Correct Answer

✅ Option d — 1:4

All Options:

  • A1:1
  • B1:2
  • C1:3
  • D1:4

Detailed Solution & Explanation

**Step 1: Set up equations.** Let number of men =m\displaystyle = m and women =w\displaystyle = w. Total =m+w=100\displaystyle = m + w = 100. **Step 2: Apply combined mean formula.** 26m+21wm+w=25\frac{26m + 21w}{m + w} = 25 26m+21w=25×100=250026m + 21w = 25 \times 100 = 2500 **Step 3: Solve the system.** From m+w=100⇒m=100−w\displaystyle m + w = 100 \Rightarrow m = 100 - w. 26(100−w)+21w=250026(100 - w) + 21w = 2500 2600−26w+21w=25002600 - 26w + 21w = 2500 2600−5w=25002600 - 5w = 2500 5w=100  ⟹  w=20,m=805w = 100 \implies w = 20, \quad m = 80 **Step 4: Compute the ratio.** wm=2080=14\frac{w}{m} = \frac{20}{80} = \frac{1}{4} So women : men =1:4\displaystyle = 1 : 4. **Note:** The computation gives ratio 1:4 (Option D), not 1:3. Verifying: 26(80)+21(20)=2080+420=2500\displaystyle 26(80) + 21(20) = 2080 + 420 = 2500 ✓. The correct ratio is **1:4**. Hence, **Option D** is the correct answer.

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