A and B can do a piece of work in 10 hours by B and C 12 hours and C A in 15 hours how long will they take if they work together how long will each take to complete the work independently
Answers
Answer:
they take together complete tha work 8 day
A take =24 day
B take= 17 1/7 day
c take= 40 day
Explanation:
Given :-
A and B can do a piece of work in 10 hours by B and C 12 hours and C and A in 15 hours.
To find :-
i)How long will they take if they work together ?
ii)How long will each take to complete the work independently ?
Solution :-
Given that :
A work completed by A and B = 10 hours
The work completed by both A and B in one hour = 1/10
A+ B = 1/10 -----(1)
The work completed by B and C = 12 hours
The work completed by both B and C in one hour = 1/12
B+C = 1/12 -----(2)
The work completed by C and A = 15 hours
The work completed by both C and A in one hour = 1/15
C+A = 1/15 -----(3)
On adding (1),(2)&(3) then
A+B+B+C+C+A = (1/10)+(1/12)+(1/15)
=> 2A+2B+2C = (1/10)+(1/12)+(1/15)
LCM of 10 , 12 and 15 = 60
=> 2A+2B+2C =(6+5+4)/60
=>2(A+B+C) = 15/60
=> 2(A+B+C) = 1/4
=> A+B+C = (1/4)/2
=> A+B+C = 1/(4×2)
=> A+B+C = 1/8----------(4)
They work together they will complete the work in one hour = 1/8
They work together,they will complete the work in 8 hours .
Now,
A can do the work independently in one hour
= (A+B+C)-(B+C)
From (4) and (2)
=> (1/8)-(1/12)
LCM of 8 and 12 = 24
=> (3-2)/24
=> 1/24
A can do the work in one hour = 1/24
A can do the work in 24 hours independently.
B can do the work in one hour independently
= (A+B+C)-(A+C)
From (4) and (3)
=> (1/8)-(1/15)
LCM of 8 and 15 = 120
=> (15-8)/120
=> 7/120
B can do the work in one hour = 7/120
B can do the work independently in 120/7 hours or 17 1/7 hours
C can do the work independently in one hour
= (A+B+C) -(A+B)
From (4)&(1)
=> (1/8)-(1/10)
LCM of 8 and 10 = 40
=> (5-4)/40
=> 1/40
C can do the work in hour is 1/40
C can do the work in 40 hours independently.
Answer:-
i)If they week together then they will take 8 hours to complete the work.
ii)
- A can complete the work in 24 days independently.
- B can complete the work in 120/7 hours or 17 1/7 hours independently.
- C can do complete the work in 40 hours independently.