In A Coaching Centre the average age of students studying for competitive exams is 22 Years. The average age of boys in the class is 26 years and that of the Girls is 19 years. If the number of boys in the class is 12. Find the number of girls in the class?
This questions was previously asked in
RRB PO Prelims (06 Aug 2023, Shift 4)
Explanation:
To find the number of girls in the class, we'll use the concept of weighted averages:
- The average age of all students is 22 years.
- The average age of boys is 26 years. There are 12 boys.
- The average age of girls is 19 years.
- Let the number of girls be \( G \).
The equation for average age becomes:
\[ \frac{(12 \times 26) + (G \times 19)}{12 + G} = 22 \]
Simplify:
\[ 312 + 19G = 22(12 + G) \]
\[ 312 + 19G = 264 + 22G \]
\[ 312 - 264 = 22G - 19G \]
\[ 48 = 3G \]
\[ G = 16 \]
- Therefore, the number of girls is \( \textbf{16} \).
- Option 3 is correct.
The correct answer is Option: 3, 16.
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By: Parvesh Mehta