Central Tendency & DispersionPYQ Dec. 21Question 2866 of 473
All Questions

If average mark for a group of 30 girls is 80, a group of boys is 70 and combined average is 76, then how many are in the boy's group?

Options

A21\displaystyle 21
B20\displaystyle 20
C22\displaystyle 22
D19\displaystyle 19
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Correct Answer

✅ Option b — 20\displaystyle 20

All Options:

  • A21\displaystyle 21
  • B20\displaystyle 20
  • C22\displaystyle 22
  • D19\displaystyle 19

Detailed Solution & Explanation

**Step 1: Set up variables.** Let the number of boys = nb\displaystyle n_b. Number of girls = 30. **Step 2: Apply combined mean formula.** xˉcombined=ng⋅xˉg+nb⋅xˉbng+nb\bar{x}_{combined} = \frac{n_g \cdot \bar{x}_g + n_b \cdot \bar{x}_b}{n_g + n_b} 76=30×80+nb×7030+nb76 = \frac{30 \times 80 + n_b \times 70}{30 + n_b} **Step 3: Solve for nb\displaystyle n_b.** 76(30+nb)=2400+70nb76(30 + n_b) = 2400 + 70n_b 2280+76nb=2400+70nb2280 + 76n_b = 2400 + 70n_b 6nb=1206n_b = 120 nb=20n_b = 20 Hence, **Option B** is the correct answer.

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