Question
40 laborers were hired to finish a construction job in
50 days. After 35 days of work, only 62.5% of the job was done. How many additional laborers are needed to finish the remaining work in the remaining time?Solution
Let the total work be W.
40 laborers working for 35 days completed 62.5% of the work.
So,
40 × 35 = 1400 laborer-days = 62.5% of W
62.5% = 5/8
So,
5/8 of W = 1400
W = 1400 × 8/5 = 2240 laborer-days
Remaining work = 100% - 62.5% = 37.5% of W
37.5% = 3/8
Remaining work = 3/8 × 2240 = 840 laborer-days
Time left = 50 - 35 = 15 days
Number of laborers needed to finish 840 laborer-days in 15 days:
840 ÷ 15 = 56 laborers
Additional laborers needed = 56 - 40 = 16
Answer:
16 additional laborers are needed.
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