Question

A and B together can do a piece of work in 8 days, but A alone can do it in 12 days. How many days would B alone take to do the same work?

Answer 1

Answer:

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 =

= 8/12

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 ..

Answer 2

Step-by-step explanation:

• (A + B) = 8 Days

• A = 12 Days

• B = ?

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf B=\dfrac{(A+B) \times A}{A-(A+B)}\\\\\\:\implies\sf B = \dfrac{8 \times 12}{12 - 8}\\\\\\:\implies\sf B = \dfrac{8 \times 12}{4}\\\\\\:\implies\sf B = 2 \times 12\\\\\\:\implies\underline{\boxed{\sf B = 24 \:Days}}$

⠀

$\therefore\:\underline{\textsf{B can alone do the work in \textbf{24 Days}}}.$