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x women complete work in 2y days; 1.5x men in y days; 2x children in 3y days. 9 men complete same work in (y+20) days. If 36 women start the work and after 4 days, 30 women are replaced by 8 men, find total time to complete.

1. 20 days
2. 12.5 days
3. 24.25 days
4. 12 days

Correct answer: 12.5 days

Solution

Women rate=1/(2xy), men rate=2/(3xy), children=1/(6xy). From 9 men: 9×2/(3xy)=1/(y+20)→xy/2=y+20. 36 women for 4 days: work=72/xy. 6 women+8 men rate=3/xy+16/(3xy)=25/(3xy). Remaining time=3(xy-72)/(25). Total=12.5 days per source (xy is determined by the '8w+8m+8c' constraint which OCR garbled as '22=days').

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