Three batches of students have average ages 17, 19, and 23 years respectively. If their numbers are in the ratio 3 : 4 : 6, what is the overall average age of all the students?

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Accepted Answer

1. Use weighted average with group sizes as weights.

2. Compute each group's total age: $3	imes17=51$, $4	imes19=76$, $6	imes23=138$.

3. Sum totals and weights: total age $=51+76+138=265$, total students $=3+4+6=13$.

4. Average $=\dfrac{265}{13}=20.3846\approx20.38$. So the correct choice is **(b)**.

FINAL_ANSWER: b

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