Minimum Initial Class Strength

Let $G$ be the initial number of girls and $B$ be the initial number of boys, with $B > 10$. After 40% girls leave, remaining girls $= 0.6G$. After 60% boys leave, remaining boys $= 0.4B$. We are given: $0.6G = 0.4B + 8 \implies 3G = 2B + 40 \implies 2B = 3G - 40$ Since $B > 10$, $2B > 20 \implies 3G - 40 > 20 \implies 3G > 60 \implies G > 20$. Also, $G$ must be an even integer for $B$ to be an integer (since $2B = 3G - 40$). To minimize total initial students $G + B$, choose the smallest even integer $G > 20$: If $G = 22$: $2B = 3(22) - 40 = 66 - 40 = 26 \implies B = 13$ Since $B = 13 > 10$, this condition is satisfied. Minimum initial number of students $= G + B = 22 + 13 = 35$.