18 women complete a work in 24 days and 24 men complete the same work in 15 days. 16 women worked for 3 days and then they left. 20 men worked for the next 2 days, and then they are joined by 16 women. In how many days will they finish the remaining work?
18 women complete a work in 24 days and 24 men complete the same work in 15 days. 16 women worked for 3 days and then they left. 20 men worked for the next 2 days, and then they are joined by 16 women. In how many days will they finish the remaining work?
Solution
Total work can be expressed in units:
- 18 women complete work in 24 days → Total work = 18 × 24 = 432 woman-days
- 24 men complete work in 15 days → Total work = 24 × 15 = 360 man-days
Using LCM of 432 and 360 = 2160 units as total work:
Work rate per person per day:
- 1 woman's 1 day work = 2160 ÷ 432 = 5 units/day
- 1 man's 1 day work = 2160 ÷ 360 = 6 units/day
Work done by 16 women for 3 days:
Work done = 16 × 3 × 5
Work done = 240 units
Work done by 20 men for 2 days:
Work done = 20 × 2 × 6
Work done = 240 units
Total work = 2160 units
Work completed = 240 + 240 = 480 units
Remaining work = 2160 - 480
Remaining work = 1680 units
Combined daily work rate when 20 men and 16 women work together:
Daily work rate = (20 × 6) + (16 × 5)
Daily work rate = 120 + 80
Daily work rate = 200 units/day
Days needed = 1680 ÷ 200
Days needed = 8.4 days
Days needed = days
Therefore, they will finish the remaining work in days.
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