Question

A and B together can do a piece of work in 8 days. If
A alone can do the same work in 12 days, then B
alone can do the same work in?​

Answer 1

Given :

• A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days

To find :

• B alone can do the same work in?

Solution :

$\sf{In \: 1 day \: \: A \: and \: B \: together \: can \: do \: \dfrac{1}{8} \: of \: the \: work}. \\ \\ \sf{In \: 1 \: day \: A \: alone \: can \: do \: \dfrac{1}{12}\: of \: the \: work.} \\ \\ \sf{\therefore \: In \: 1 \: day \: B \: alone \: can \: do \: \dfrac{1}{8} - \dfrac{1}{12} \: of \: the \: work, \: ie, \: of \: the \: work.} \\ \\ \sf{\therefore \:B \: alone \: will \: take \: \dfrac{1}{ \dfrac{1}{24} },} \\ \\ \sf{ i.e., 24 \: days \: to \: do \: the \: work}$

Answer 2

Answer:

• (A + B) = 8 Days
• A = 12 Days
• B = ?

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

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

⠀

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