Central Tendency & DispersionMTP March 22Question 2905 of 473
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If average marks for a group of 30\displaystyle 30 girls is 80\displaystyle 80, a group of boys is 70\displaystyle 70 and combined average is 76\displaystyle 76, then how many boys are in the group ?

Options

A21
B20
C22
D19
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Correct Answer

✅ Option b — 20

All Options:

  • A21
  • B20
  • C22
  • D19

Detailed Solution & Explanation

**Step 1: Let number of boys = nb\displaystyle n_b.** Combined mean=30×80+nb×7030+nb=76\text{Combined mean} = \frac{30 \times 80 + n_b \times 70}{30 + n_b} = 76 **Step 2: Solve.** 2400+70nb=76(30+nb)=2280+76nb2400 + 70n_b = 76(30 + n_b) = 2280 + 76n_b 2400−2280=76nb−70nb2400 - 2280 = 76n_b - 70n_b 120=6nb120 = 6n_b nb=20n_b = 20 **Note:** The computed number of boys is **20** (Option B), not 19 (Option D). Verification: (30×80+20×70)/(30+20)=(2400+1400)/50=3800/50=76\displaystyle (30 \times 80 + 20 \times 70)/(30+20) = (2400+1400)/50 = 3800/50 = 76 ✓ Hence, **Option B** is the correct answer.

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