Question

A and B together can finish a piece of work in 2days if A alone can finish the same work in 20 days in how many days B alone can finish it ​

Answer 1

Answer :-

B alone can finish same work in 2.23 days.

Solution :-

A and B can finish a piece of work in 2 days

So A and B one day work = 1/2

A alone can finish same work in 20 days

So A's one day work = 1/20

Let the B's one day work be 1/B

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

⇒ 1/B = 1/2 - 1/20

Taking LCM

⇒ 1/B = (10 - 1)/20

⇒ 1/B = 9/20

⇒ B = 20/9

⇒ B = 2.23

Therefore B alone can finish same work in 2.23 days.

Answer 2

$\bold {\huge {Answer :-}}$

$\bf\huge\boxed{\frac{20}{9} \:days }$

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✦Given

➛A & B together can finish a wirk in 2 days

➛A alone can finish the same work in 20 days

✦To Find

➛B alone can finish the same work in how many days

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Step-By-Step Explaination

A & B together do the work in 2 days

→(A + B)'s one day work = 1/2

A can do in 20 days alone

→A' s one day work = 1/20

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So, we got two equation

⇲$\Large\bold{A + B = \frac{1}{2}}$ ______(1)

⇲$\Large\bold{A= \frac{1}{20}}$ _______(2)

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

$\Large\bold{\therefore\:\frac{1}{20} + B= \frac{1}{2}}$

$\Large\bold{\Rightarrow\:B= \frac{1}{2}-\frac{1}{20}}$

$\Large\bold{\Rightarrow\:B=\frac{9}{20}}$

Since, B does $\Large\bold{\frac{9}{20}}$ part of the work

[in one day]

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Therefore,B can alone finish the same work in $\Large\bold{\boxed{\boxed{\frac{20}{9} }}}$ days