Question

A and b working separately can do a piece of work in 9 and 12 days respectively. if they work for a day alternately, a beginning, in how many days, the work will be completed?

Answer 1

Solution :

_____________________________________________________________


Given :

A & B working separately  can do a piece of work in 9 days & 12 days respectively.

_____________________________________________________________

To find :

If they work for a day alternatively they the time taken to complete the piece of work.

_____________________________________________________________

If A takes 9 days to complete the piece of work,.

The amount of work completed in 1 day = $\frac{1}{9}$ th of total work,.

___________________________

If B takes 12 days to complete the pice of work,.

Similarly,.

The amount of work completed in 1 day = $\frac{1}{12}$

_____________________________________________________________

If they work alternatively, with A as begining,

Then,

$\frac{1}{9} + \frac{1}{12} + \frac{1}{9} + \frac{1}{12} + \frac{1}{9} + \frac{1}{12} ,.. = 1$

Hence, the number of days be 2x+1,.

Then, the days that A work = x + 1 days
The days that B works = x days

Then,

$( \frac{1}{9} )(x + 1) + (\frac{1}{12}) (x) = 1$

⇒ $\frac{x+1}{9} + \frac{x}{12} = 1$

⇒ $\frac{4(x+1)+3(x)}{36} = 1$

⇒ $\frac{4x+4+3x}{36}$

⇒ $\frac{7x+4}{36} = 1$

⇒ $7x + 4 = 36$

⇒ 7x = 36 - 4

⇒ 7x = 32

⇒ x ≈ 5 days,.

The total number of days = 2x + 1

⇒ 2(5) + 1

⇒ 10 + 1

⇒ 11 days,.

_____________________________________________________________

                                  Hope it Helps!!

⇒ Mark as Brainliest,.