Central Tendency & DispersionMTP June 2023 Series IIQuestion 2915 of 473
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The average age of 15\displaystyle 15 numbers in a class is 9\displaystyle 9 years. Out of them, the average age of 5\displaystyle 5 students is 13\displaystyle 13 years and that of 8\displaystyle 8 students is 5\displaystyle 5 years. What is the average of remaining 2\displaystyle 2 students?

Options

A25\displaystyle 25 years
B9\displaystyle 9 years
C10\displaystyle 10 years
D15\displaystyle 15 years
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Correct Answer

✅ Option d — 15\displaystyle 15 years

All Options:

  • A25\displaystyle 25 years
  • B9\displaystyle 9 years
  • C10\displaystyle 10 years
  • D15\displaystyle 15 years

Detailed Solution & Explanation

**Step 1: Total sum of ages of all 15 students.** Total=15×9=135\text{Total} = 15 \times 9 = 135 **Step 2: Sum of the two known groups.** - Group 1 (5 students, avg = 13): sum =5×13=65\displaystyle = 5 \times 13 = 65 - Group 2 (8 students, avg = 5): sum =8×5=40\displaystyle = 8 \times 5 = 40 **Step 3: Sum of remaining 2 students.** Remaining =15−5−8=2\displaystyle = 15 - 5 - 8 = 2 students. Sum of remaining=135−65−40=30\text{Sum of remaining} = 135 - 65 - 40 = 30 **Step 4: Average of remaining 2.** Average=302=15\text{Average} = \frac{30}{2} = 15 **Note:** The computed average is **15** (Option D), not 10 (Option C). Hence, **Option D** is the correct answer.

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