A job can be completed by 2 men, 3 women and 4 children in 15 days. The same work, can be completed by 9 women and 6 children in 10 days. If 1 man and 1 woman can complete it in 48 days . Find the time in which one man can complete it. ( in days)

Options

A. 60
B. 75
C. 80
D. 90

Answer

C

Explanation

Let the work which can be completed each day by each man, each women and each child be m units, w units and t units respectively.
Work which two, men three women and four childrn can complete `=(2m+3w+4c)` units
`:. Job=(2m+3w+4c)(15)` units
`=(9w-6c)(10)` unis `=(m+w)(48)` units
`(2m+3w+4c)(15)=(9w+6c)(10)`
`30m+45w+60c=90w+60c`
`30m=45w`
`m=(3)/(2)w,`
`:. Job=((3)/(2)w+w)(48)` units
`120w` units
Time in which a man can complete it `=(120w)/((3)/(2)w)"days"=80 "days"`