Question

At the Lok Sabha, the average age of the M male MPs is F and the average age of F female MPs is M. If the average age of everyone, including the 42-year-old Speaker Sumitra Mahajan (assume she is not MP), is M+F.
The numerical value of M+F is ___

Answer 1

Given that the combined average is M+F, hence

$(M+F)=\frac{(2MF+42)}{\left\{\right(M+F)+1\}}$

Or $(M+F{)}^2+(M+F)=2MF+42$

Or $M^2+F^2+M+F=42$

Or $M(M+1)+F(F+1)=42,$ since M and F are integers, there is only one possibility that M(M+1) =12 or 30 and F(F+1) =30 or 12. Hence M can be 3 or 5 and F can be 5 or 3. So the sum of M and F is 8.