A, B and C can mow a field in 36 days, 72 days and 54 days respectively. All the three began the work together on January 1, 2016, but A left 8 days and C 12 days before the completion of the work. If B took the rest for 4 days, then in how many days the work was finished from the day it started?

Let work be completed in x days. Then, Work done by A in (x-8) days + work done by B in x days + work done by C in (x-12) days = 1 (x-8)/36 + x/72 + (x-12)/54= 1 ⇒(6(x-8)+ 3x+4(x-12))/216 = 1⇒(6x-48+3x+4x-48)/216 = 1 ⇒(13x-96)/216 = 1 ⇒ 13 x – 96 = 216 ⇒ 13 x = 312 ⇒x = 24 days ∴ Total days = 24 days Since B takes rest for 4 days, so the number of days in which the work was finished from the day it started = 24 + 4 = 28 i.e., on 28th January 2016.

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