The work done by a women in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same work, working 8 hours per day ?

Answer: Option A

Ratio of time taken by a woman, a man and a boy
$$\begin{array}{rl}& =8:6:12\\ & =4:3:6\end{array}$$
So, 4 women ≡ 3 men ≡ 6 boy
(12 mens + 12 womens + 12 boys)
$$\begin{array}{rl}& =\left[12+\left(\frac{3}{4}\times 12\right)+\left(\frac{3}{6}\times 12\right)\right]\text{men}\\ & \text{ = }\left(12+9+6\right)\text{men}\\ & =27\text{ men}\end{array}$$
Let the required number of days be x
More men, Less days (Indirect proportion)
More working hours, Less days (Indirect proportion)
$$\begin{array}{c}\text{Working hours 8}:6\text{hfill}\\ \text{Men 27}:9\text{hfill}\end{array}\}::6:x$$
$$\begin{array}{rl}& \therefore 27\times 8\times x=9\times 6\times 6\\ & \iff x=\frac{\left(9\times 6\times 6\right)}{\left(27\times 8\right)}\\ & \iff x=\frac{3}{2}\\ & \iff x=1\frac{1}{2}\end{array}$$