Question:A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together all will finish the work in :
A `13 1/3` days
B `15` days
C `20` days
D `30` days
+ Explanationsolution:
`C`alone can finish the work in `40` days.
`:. (A + B)` can do it in `20` days.
`:. (A + B)'s 1` day's work `= 1/20`.
`A's 1` day's work : `B's 1` day's work `= 1/2 : 1`
`= 1 : 2`.
`:. A's 1` day's work `= (1/20 xx 1/3)`
`= 1/60`. [Divide `1/20` in the ratio 1 : 2]
`B's 1` day's work `= (1/20 xx 2/3)`
`= 1/30`.
`(A + B + C)'s 1` day's work `= (1/60 + 1/30 + 1/40)`
`= 9/120`
`=3/40`.
`:.` All the three together will finish it in `40/3`
`=13 1/3` days.
