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?

Solution

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 [if gte msEquation 12]> x -8 36 [if !msEquation]-->[endif]-->`(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` ⇒ [if gte msEquation 12]> 13x-96 216 [if !msEquation]-->[endif]-->`(13x-96)/216` = 1 ⇒ 13x – 96 = 216 ⇒ 13x [if gte msEquation 12]> x [if !msEquation]-->[endif]-->= 312 ⇒ [if gte msEquation 12]>x [if !msEquation]-->[endif]-->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 28 ^th January 2016