8 children and 12 men complete a certain piece of work in 9 days. If each child is half as efficient as man, then in how many days will twelve men finish this same work ?

8C=4M
now
(8C+12M)*9=12M*x
=>16M*9=12M*x
=>x=12

the answer is 21 days right?

Assume that total work do be is 1 unit.
Given eff(C) = 1/2*eff(M) -> 8*eff(C) = 8*1/2*eff(M) -> 8*eff(C) = 4eff(M)-> eff(8C) = eff(4M)
Rate of work -> eff(8C+12M) = 1/9 units/day
eff(8C) + eff(12M) = 1/9 -> eff(4M) + eff(12M) = 1/9 => eff(M) = 1/9 * 1/16
eff(12M) = 12*eff(M) -> 12*1/9*1/16 = 1/12
Hence, 12 Men would complete 1/12th part of work in 1 day => Therefore, they would require 12 days to complete the entire work.