Question

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?

Answer 1

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,

⇒ $x + y = \frac{1}{30}$  ...(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,

⇒ $11x +11y = \frac{11}{30}$  (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,

⇒ $28x = 1 - \frac{11}{30} = \frac{30 - 11}{30} = \frac{19}{30}$

⇒ $28x = \frac{19}{30}$

⇒ $x = \frac{19}{28 \times 30} = \frac{19}{840}$

∴ Work done by 'a' in 1 day = $\frac{19}{840}$

∴ time taken for 'a to complete work by himself is,

⇒ $\frac{840}{19}$≈ 45 days