A and B together can complete a piece of work in 24 days, B and C can do it in 40 days and C and A can do it in 30 days. A, B and C alone can complete it in
Answers
Answer:
Step-by-step explanation:
Let Total work is = x
(A + B) takes 30 days to complete x work
work done by (A+B) in 1 day = x/30
(B+C) takes 24 days to complete x work
=> work done by (B+C) in 1 day = x/24
(A+C) takes 40 days to complete x work
=> work done by (A+C) in 1 day = x/40
work done by (A+B)+(B+C)+(A+C) in 1 day = x/30 + x/24 + x/40 = x(4+5+3)/120
work done by 2(A+B+C) in 1 day = 12x/120
= x/10
work done by (A+B+C) in 1 day = x/20
Time taken by (A+B+C) to complete the x work =
= {Total work / work done by (A+B+C) in 1 day}
= {x/x/20} = 20
Time taken by (A+B+C) to complete the total work(x) = 20 Days
Now, Calculating seperately work done by each
=>
Work done by A in 1 day =
= {work done by (A+B+C) in 1 day - work done by (B+C) in 1 day}
= {x/20 - x/24} = x{6–5}/120
= x/120
Time taken by A to complete the work
= (Total work/Work done by A in 1 Day)
= x/x/120 = 120 Days
Time taken by A to complete the work
= 120 Days
Work done by B in 1 day =
= {work done by (A+B+C) in 1 day - work done by (A+C) in 1 day}
= {x/20 - x/40} = x{2–1}/40
= x/40
Time taken by B to complete the work
= (Total work/Work done by B in 1 Day)
= x/x/40 = 40 Days
Time taken by B to complete the work
= 40 Days
Work done by C in 1 day =
= {work done by (A+B+C) in 1 day - work done by (A+B) in 1 day}
= {x/20 - x/30} = x{3–2}/60
= x/60
Time taken by C to complete the work
= (Total work/Work done by C in 1 Day)
= x/x/60 = 60 Days
Time taken by C to complete the work
= 60 Days
Now,
Time taken by (A+B+C) to complete the work = 20 Days
Time taken by A to complete the work = 120 Days
Time taken by B to complete the work = 40 Days
Time taken by C to complete the work = 60 Days
Short Trick for such questions is assume Total work = LCM of All combination to complete the work
=> Total work = 120
Work done by (A+B)/day = 120/30 = 4
Work done by (B+C)/day = 120/24 = 5
Work done by (A+C)/day = 120/40 = 3
Work done by {(A+B)(B+C)(A+C)}/day =
= 4+5+3 = 12
Work done by (A+B+C)/day = 12/2 = 6
Time Taken by(A+B+C) = 120/6 = 20Days
Time Taken by(A+B+C) = 20Days
Work done by A/day =
= {Work done by (A+B+C)/day -Work done by (B+C)/day} = 6 - 5 = 1
Time Taken by A = 120/1 = 120 Days
Time Taken by A = 120 Days
Work done by B/day =
= {Work done by (A+B+C)/day -Work done by (A+C)/day} = 6 - 3 = 3
Time Taken by B = 120/3 = 40 Days
Time Taken by B = 120 Days
Work done by C/day =
= {Work done by (A+B+C)/day -Work done by (A+B)/day} = 6 - 4 = 2
Time Taken by C = 120/2 = 60 Days
Time Taken by C = 60 Days