4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can do it in 10 days. To complete the same work in 7 days, how many women should assist 4 men?
13
Step 1 — Equate the two work expressions:
Let one man's daily work be \(M\) and one woman's be \(W\). Since the same work is done in both cases:
\[(4M+5W)\times 15 = (9M+6W)\times 10\]
Step 2 — Find the man-woman ratio:
\[60M+75W = 90M+60W \implies 15W = 30M \implies W = 2M\]
Step 3 — Total work in man-units:
\[(4M+5\cdot 2M)\times 15 = 14M\times 15 = 210M\]
Step 4 — Set up the 7-day scenario:
Let \(x\) women assist 4 men. Then:
\[(4M + x\cdot 2M)\times 7 = 210M\]
\[(4+2x)\times 7 = 210 \implies 4+2x = 30 \implies x = 13\]
Therefore 13 women are required.
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