Math, asked by praneeth3513, 11 months ago

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?


sivaprasath: is it 38 days or 28 days ?

Answers

Answered by sivaprasath
6

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

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