A person wants to get a piece of work done. There are 2 workers 'A' and 'B'. 'A' said I will take 8 days less than the time taken by 'B' to finish the piece of work. If both 'A' and 'B' together do the same piece of work, they can finish it in 3 days. Find the time taken by 'B' alone to finish the work.
Answers
Answered by
3
Let B takes x days to complete the work.
B's 1 day work =1/x.
Then ,A takes (x-8) days to complete the work.
A's 1 day work=1/(x-8)
A and B can complete the work in 3
days .
(A andB)'s 1 day work=1/3
=>x+1/(x-8)=1/3
=>(x-8+x)3=x(x-8)
=>6x-24=x^2-8x
=>x^2-14x+24=0
=>(x-2)(x-12)=0
=>x=2 or x=12
If x=2 ,then A will take (x-8)=-6days
which is impossible as time is a
fundamental quantity so,it can't be
-ve .Hence,x=12
B takes =12 days and A takes =4 days
B's 1 day work =1/x.
Then ,A takes (x-8) days to complete the work.
A's 1 day work=1/(x-8)
A and B can complete the work in 3
days .
(A andB)'s 1 day work=1/3
=>x+1/(x-8)=1/3
=>(x-8+x)3=x(x-8)
=>6x-24=x^2-8x
=>x^2-14x+24=0
=>(x-2)(x-12)=0
=>x=2 or x=12
If x=2 ,then A will take (x-8)=-6days
which is impossible as time is a
fundamental quantity so,it can't be
-ve .Hence,x=12
B takes =12 days and A takes =4 days
Similar questions
Social Sciences,
7 months ago
Computer Science,
7 months ago
English,
7 months ago
World Languages,
1 year ago