15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, 3 women do as much work as 2 men ?

3 women ≡ 2 men
So, 21 women ≡ 14 men
Less men, More days (Indirect proportion)
Less hours per day, More days (Indirect proportion)
\[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 14}}:15 \hfill \\ {\text{Hours per day 6}}:8 \hfill \\ \end{gathered} \right\}::21:x\]
$$\eqalign{ & \therefore \,\left( {14 \times 6 \times x} \right) = \left( {15 \times 8 \times 21} \right) \cr & \Leftrightarrow x = \frac{{\left( {15 \times 8 \times 21} \right)}}{{\left( {14 \times 6} \right)}} \cr & \Leftrightarrow x = 30 \cr} $$
∴ Required number of days = 30