Three men, four women and six children can complete a work in seven days. A woman does double the work a man does, and a child does half the work a man does. How many women alone can complete this work in 7 days?

7 women alone can finish it in 7 days.

Take a man's daily work as 1 unit; then a woman = 2 units and a child = 0.5 unit.

Daily work = 3 x 1 + 4 x 2 + 6 x 0.5 = 3 + 8 + 3 = 14 units.

Total work = 14 x 7 = 98 unit-days.

In 7 days each woman gives 2 x 7 = 14 units, so 98 / 14 = 7 women.