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A group of men decided to do a job in 8 days. But since 10 men dropped out after 1st day, 2 more men dropped out after 2nd day, 2 more men dropped out after 3rd day and so on, the job got completed at the end of 12th day. How many men were there at the beginning?   55     56     57     58
Asked by 105236 | 31 Aug, 2021, 06:26: PM
Let x men in group . If work is to be completed in 8 days , then number of man-days = 8x

Man-days in each day is tabulated below

 day 1 2 3 4 5 6 7 8 9 10 11 12 Man-day x x-10 x-12 x-14 x-16 x-18 x-20 x-22 x-24 x-26 x-28 x-30

sum of man-days , 8x = x +(x-10) + (x-12) + (x-14) + (x-16) + (x-18) + (x-20) + (x-22) + (x-24) + (x-26) + (x-28) +(x-30)

8x = 12 x  - ( 10 + 12+ 14 ...................... +28+30 )

8x = 12 x - [ (11/2) ( 10 + 30 ) ] = 12 x - 220

From above expression, we get , x = 55

Hence , there were initially 55 men in the group

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