Question

A and B working together can finish a piece of work in 12 days while A alone can finish it in 30 days in how many days can B alone finish the work?​

Answer 1

$\bold {\huge {Your ~answer :-}}$

$\bf\huge\boxed{20\:days }$

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EXPLAINATION ➣

A & B together do the $\green{\texttt{ work in 12 days}}$

⁃(A + B)'s one day work = 1/12

A can do in $\green{\texttt{ 30 days alone}}$

⁃A' s one day work = 1/30

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So, we got two equation

⇲ A + B = 1/12 ______(1)

⇲ A = 1/30 _______(2)

$\green{\texttt{ Substituting}}$eq(2) in eq(1)

⇨ 1/30 + B = 1/12

⇒B = 1/12 - 1/30

⇒B = 3/60 = 1/20

Since, B does 1/20 part of the work

Therefore, $\green{\texttt{B can alone finish }}$

$\green{\texttt{ the work in 20 days }}$

#Verified answers

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Answer 2

Answer:

B alone can complete the work in 20 days.

Step-by-step explanation:

Given that :

A and B working together can finish a piece of work in 12 days.

To Find :

In how many days can B alone finish the work.

Solution :

$\bigstar$ Consider as -

A finish the work as A days. B finish the work as B days.

Then,

A can do $\sf \dfrac{1}{A}$ work in a day.

B can do $\sf \dfrac{1}{B}$ work in a day.

Therefore,

A and B can do $\sf \dfrac{1}{A} + \dfrac{1}{B}$ work in a day.

As given,

Both can do the work in 12 days.

A can complete the work in 30. A can do $\sf \dfrac{1}{A}$ work in a day.

So,

$\sf \implies \dfrac{1}{A} + \dfrac{1}{B} = \dfrac{1}{12}........Eq(1)$

$\sf \implies \dfrac{1}{A} =\dfrac{1}{30}.......Eq(2)$

Both in 1 Equation,

$\tt \implies \dfrac{1}{2} - \dfrac{1}{30}\\ \\\implies \dfrac{5-2}{60}\\ \\\implies \dfrac{3}{60}\\ \\\implies \dfrac{1}{20}$

∴ B alone can complete the work in 20 days.