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No of workdays W is 44 man-days

Total number of man-days = (2 + 1/2 + 1/4) * Days

Number of days = 44/11*4 = 16

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You made a typo while mentioning the calculation of the number of days; request you to please fix it.
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Let the efficiency of each man is x. Now,each person works in one day 1/x amount. Now four mem do 4*1/x=4/x
Atq,4/x= 1/11, after calculating we get x=44.
Now as two men work half time and quarter time, and other two men work full time, so we can get working amount of each day by four men, which is
1/44 + 1/44 + 1/88 +1/176 = 11/176 (working amount) . After reversing 176/11, we get 16. Here 16 is the number of days. Thus answer is 16 days.

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Assume total work is 1 unit
Case 1: 4 ppl worked then rate per man is work/time I.e R= 1/(11*4) given 11 days to finish 1 unit work.
Case 2: let time taken T days, amount of work is same ie 1 unit,
Work = sum of rate of each person* time
1=T( (1/44)+(1/44)+ (0.5*1/44)+(0.25*1/44) )
on simplifying we get T=16

Hope this is helpful !!!
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