Question

A and B together can do a work in 12 days . Which A alone can do it in 30 days. In how many days B alone can do it .​

Answer 1

Answer:

20 days.

Step-by-step explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• A and B can do a work in 12 days.
• A alone can do it in 30 days.

$\underline{\bigstar\:\textsf{To\:find:}}$

• In how many days B can do it = ?

$\underline{\bigstar\:\textsf{Solution:}}$

We know that A and B both can work in 12 days. So, work done by both in one day will be $\dfrac{1}{12}$.

Now, A can alone do work in 30 days. So, work done by A in one day will be $\dfrac{1}{30}$

$\:$

Our equation will be -

$\:$

$\Longrightarrow\:\sf{A\:+\:B\:=\:\dfrac{1}{12}}$

$\:$

$\Longrightarrow\:\sf{\dfrac{1}{30}\:+\:B\:=\:\dfrac{1}{12}}$

$\:$

$\Longrightarrow\:\sf{B\:=\:\dfrac{1}{12}\:-\:\dfrac{1}{30}}$

$\:$

$\Longrightarrow\:\sf{B\:=\:\dfrac{30\:-\:12}{360}\:\:\:\:\:\:\:\:\:\:(Take\:L.C.M.)}$

$\:$

$\Longrightarrow\:\sf{B\:=\:\cancel{\dfrac{18}{360}}}$

$\:$

$\Longrightarrow\:\sf{B\:=\:\dfrac{1}{20}}$

$\:$

$\sf{\underline{\underline{\therefore\:B\:alone\:can\:do\:the\:work\:in\:20\:days.}}}$

Answer 2

GiveN :-

• A and B can do a work in 12 days.

• A alone can do it in 30 days.

To FinD :-

• In how many days B can do this work

SolutioN :-

• We know that A and B both can work in 12 days. So, work done by both in one day will be $\dfrac{1}{12}$

• Now, A can alone do work in 30 days. So, work done by A in one day will be $\dfrac{1}{30}$

Our equation will be -

$\Longrightarrow\:\sf{A\:+\:B\:=\:\dfrac{1}{12}} \\ \\ \Longrightarrow\:\sf{\dfrac{1}{30}\:+\:B\:=\:\dfrac{1}{12}} \\ \\ \Longrightarrow\:\sf{B\:=\:\dfrac{1}{12}\:-\:\dfrac{1}{30}} \\ \\ \Longrightarrow\:\sf{B\:=\:\dfrac{30\:-\:12}{360}} \\ \\ \Longrightarrow\:\sf{B\:=\:\cancel{\dfrac{18}{360}}} \\ \\ \Longrightarrow\:\sf{B\:=\:\dfrac{1}{20}}$

$\therefore\:\underline{\bf \green{B\:alone\:can\:do\:the\:work\:in\:20\:days}}$