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A contract is to be completed in 56 days and 104 men were set to work each working 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional men may be employed, so that the work may be completed in time, each man now working 9 hours day?
60
56
70
42
Persons worked (M1) = 104 Number of hours each person worked per day (H1) = 8 Number of days they worked (D1) = 30 Work completed (W1)= 2/5 Remaining days (D2)= 56 - 30 = 26 Remaining Work to be completed (W2)= 1 - 2/5 = 3/5 Let the total number of persons who do the remaining work (M2) = x Number of hours each person needs to be work per day (H2) = 9
M1D1H1W1 = M2D2H2W2 ⇒ 104×30×8 (25) = x×26×9 (35)
⇒104×30×82 = x×26×93
⇒52×30×8 = x×26×3
⇒2×30×8 = 3x
⇒x = 2×10×8 =160
Number of additional persons required = 160 - 104 = 56
Hence, option 2 is the correct answer.
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