A and b can complete a task in 30 days while working together. After a and b have been working together in 11 days, b is called away and a, complete the task all by himself in the next 28 days. If a has to work alone then in how many days the work will be completed?
Answers
Answer:
45 days
Step-by-step explanation:
Given :
'a' and b can complete a task in 30 days while working together.
After a and b have been working together in 11 days,
b is called away and a,
complete the task all by himself in the next 28 days.
If a has to work alone then in how many days the work will be completed?
Solution :
Statement 1 :
'a' and b can complete a task in 30 days while working together.
Let the total work done by a in 1 day be x,
Let the total work done by b in 1 day be y,.
Then,
⇒ 30x + 30y = 1 ( whole work done = 1)
__
In one day,
⇒ ...(i)
__
Statement 2 :
After a and b have been working together in 11 days,
b is called away and a,
complete the task all by himself in the next 28 days.
Work done in 11 days,
⇒ (from (1) )
After that,
'a' works alone to complete the remaining work in 28 days,.
⇒ work done by a in 28 days = remaining work = total - work already completed,
⇒
⇒
⇒
∴ Work done by 'a' in 1 day =
∴ time taken for 'a to complete work by himself is,
⇒ ≈ 45 days