Three men, four women and six children can complete a work in 7 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?
Answer: A
Let a man's one day work be x. Then a woman's work is 2x and a child's work is x/2. Total work done in 1 day = \(3x + 4(2x) + 6(x/2) = 3x+8x+3x = 14x\). Total work = \(14x \times 7 = 98x\). We need to find how many women can complete this in 7 days. Let the number of women be W. Their one day's work is \(W \times 2x\). Total work done by them in 7 days = \(W \times 2x \times 7 = 14Wx\). Equating the total work: \(14Wx = 98x \Rightarrow 14W=98 \Rightarrow W=7\). So, 7 women are needed.