5 ) a contractor agrees to finish a work in 46 days , and engaged 117 man working 8 hours a day. after 33 days only 4/7 of the work could be completed. he increased the work hours to 9 and additional man were engaged to finish the work in stipulated time and finished. find the additional number of man engaged.
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Remaining work
= (1−47) = 37
Remaining period = (46 - 33) = 13 days
Let the total men working at it be x
Less work, Less men (Direct proportion)
Less days, More men (Indirect proportion)
More hour/day, Less men (Indirect proportion)
Work 47:37Men 13:33Hour/day 9:8⎫⎭⎬⎪⎪⎪⎪::117:x
∴ 47×13×9×x=37×33×8×117⇔x=(3×33×8×117)(4×13×9)⇔x=198
∴ Addition men to be employed = (198 - 117) = 81
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