8. A, B and C can do a piece of work in 10 days. A alone can do it in 40 days, and B alone can do it in 30 days. In how many days will C alone do the same work?
Answers
A, B and C can do piece of work in 10 days
so they can do 1/10 part of work in a day
A alone can do same work in 40 days
so A can do 1/40 part of work in a day
B alone can do it in 30 days
so B can do 1/30 part of work in a day
let the days taken by C be x
1/10=1/40+1/30+1/x
1/10=7/120+1/x
1/10-7/120=1/x
12-7/120=1/x
5/120=1/x
1/24=1/x
therefore C can do 1/24 in a day
so C can do whole piece of work in 24 days
Answer:
The C alone will take 24 days to complete the same work
Step-by-step Explanations :
Given : A, B and C can do a piece of work in 10 days.
A alone can do it in 40 days and ,
B alone can do it in 30 days.
To find : In how many days will C alone do the same work = ?
From the given condition we can say that ,
Work done by A alone per day = 1/40
Work done by B alone per day = 1/30
So, Let the work done by C alone per day = 1/x
1/40 + 1/30 + 1/x = 1/10 ---------------- ( given )
1/x = 1/10 - [ 40 + 30 / 1200 ]
= 1/10 - [ 70/1200]
= 1/10 - 7/120
= 120 - 70 / 1200
= 50/1200 = 5/120
= 1/24
1/x = 1/24
So, x = 24 days
Hence the C alone will take 24 days to complete the same work