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Earlier discussion
1 older comment kept for context.
Oluwaseun Adeyemi
Let sum of ages of 7 pupils be \(\sum P_7 = P_7\) (left)
Let sum of ages of 25 pupils be \(\sum P_{25} = P_{25}\)
Let sum of ages of 6 pupils be \(\sum P_6 = P_6\) (joined)
\(\cfrac{P_7}{7}=12 \Rightarrow P_7 = 7 \times 12 = 84\)
\(\cfrac{P_{25}}{25}=14 \Rightarrow P_{25} = 25 \times 14 = 350\)
\(\cfrac{P_6}{6}=11 \Rightarrow P_6 = 6 \times 11 = 66\)
New average \(= \cfrac{350-84+66}{25-7+6}=\cfrac{332}{24}\)
\(=13\frac{5}{6}\)yrs \(+ \left( \cfrac{5}{6} \times 12 \right)\) months
= 13 yrs, 10 months