Question

A and b togther can finish a piece of work in 12days if A alone find sh in 20days in how many days b can finish it​

Answer 1

Given :

A and B together can finish the work in = 12 days

A and B's one day work = 1 / 12

A alone can do it in = 20 days

A's one day work = 1 / 20

We know that

B's one day works = A and B's one day work - A's one day work

= 1 / 12 - 1 / 20

Taking LCM

= ( 5 - 3 ) / 60

= 2 / 60

= 1 / 30

i e B's one day work = 1 / 30

Therefore B can finish it in 30 days

Answer 2

Answer:

$\frak{ Given}\begin{cases}\textsf{(A + B)'s Work = 12 Days}\\\textsf{A's Work = 20 Days}\\\textsf{B's Work = ?}\end{cases}$

$\rule{150}{1}$

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

$:\implies\sf (A+B)'s\:work=\dfrac{A\times B}{A+B}\\\\\\:\implies\sf 12=\dfrac{20 \times B}{20+B}\\\\\\:\implies\sf 3 = \dfrac{5 \times B}{20 + B}\\\\\\:\implies\sf 3(20 + B) = 5B\\\\\\:\implies\sf 60 + 3B = 5B\\\\\\:\implies\sf 60 = 5B - 3B\\\\\\:\implies\sf 60 = 2B\\\\\\:\implies\sf \dfrac{60}{2} = B\\\\\\:\implies\underline{\boxed{\sf B = 30\:Days}}$

⠀

$\therefore\:\underline{\textsf{B can do that work in \textbf{30 Days}}}.$