Question

'A' alone can finish a piece of work in 8 days & 'B' can alone can do it in 12 days.How much time will be taken if both 'A'&'B' work together?​

Answer 1

Answer:

See below.

Step-by-step explanation:

A and B together take 8 days [ Here ‘A’ and ‘B’ refers to the work done by ‘A’ and ‘B’] .

A takes 12 days .

So,

Let the work done by A ( in 1 day ) be one -twelfth(1/12) of the work done ..

so,

in 8 days =

8 × 1/12

= 8/12

So.. now we can say that A has done 1/8 of the work ..and B has done 1/B of the work .

1/A + 1/B = 1/12 [Here B refers to number days taken by B to do the work ]

1/8+ 1/B = 1/12

1/B = 1/24

[ We equate the denominators as the numerators are equal ]

No of days B takes to complete the work = 24 days ..

Hope this helps..Thank you for the request

Answer 2

Answer:

Step-by-step explanation:

'A' alone can finish a piece of work in 8 days

A's one day's work = $\frac18$

'B' alone can finish a piece of work in 12 days

B's one day's work = $\frac {1}{12}$

Thus one day's work of  A and B

$= \frac 18 +\frac {1}{12}\\\\=\frac {3+2}{24}\\\\=\frac {5}{24}$

Hence No of days taken by A and B to complete the work

$=\frac {1} {\frac{5}{24}}\\\\=\frac {24}{5}\\\\=4.8 \ days$