Question

08 A Casa do a piece of work in 4. houss, B and (together lando
it in 3 hours wille Aand Ctogether ten do it ih2 hours,
How long wille B Alone take to dott?

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Answer 1

Correct Question :

A and B can together do a work in 4 hours. B and C together can do it in 3 hours while A and C together can do it in 2 hours.

How long will B alone take to do it?

Solution :

A and B can together do a work in 4 hours.

So in 1 hour, A and B can do 1/4 th of the total work.

B and C can together do a work in 3 hours.

So in 1 hour, B and C can do 1/3 th of the total work.

A and C can together do a work in 2 hours.

So in 1 hour, A and C can do 1/2 th of the total work.

Adding all these equations :

> 2[ A + B + C ] can do 1/4 + 1/3 + 1/2 th of the work in 1 hour

> (  13/12 ) th

> A + B + C can do  13/24 th of the work in one hour .

So, A + B + C can take 1 11/24 th of an hour to complete the work.

Subtracting this from A + C ;

> B can do the work in | ( 1 11/24 - 2 ) | hours .

> 24/13 hours .

This is the required answer.

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Answer 2

☆ Correct Statement :-

• A can do a piece of work in 4 hours, B and C together can do it in 3 hours while Aand C together can do it in 2 hours. How long will B alone take to do it?

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☆ Given:-

• A can do a piece of work in 4 hours.
• B and C together can do it in 3 hours.
• A and C together can do it in 2 hours.

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☆ To Find:-

• Time taken by B alone to do it

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☆ Solution:-

¤ Let a, b & c be the number of hours taken by A, B & C to complete the work alone.

$\sf \:  ⟼ Given, \: A \: can \: do \: a \: piece \: of \: work \: in \: 4 \: hours.$

$\bf\implies \:\dfrac{1 }{a} = \dfrac{1}{4} \sf \:  ⟼ \: (1)$

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$\sf \:  ⟼B \: and \: C \: together \: can \: do \: it \: in \: 3 \: hours$

$\bf\implies \:\dfrac{1}{b} + \dfrac{1}{c} = \dfrac{1}{3} \sf \:  ⟼ \: (2)$

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$\sf \:  ⟼A \: and \: C \: together \: can \: do \: it \: in \: 2 \: hours$

$\bf\implies \:\dfrac{1}{a} + \dfrac{1}{c} = \dfrac{1}{2}$

$\sf \:  ⟼\dfrac{1}{4} + \dfrac{1}{c} = \dfrac{1}{2} \: \: ( \because \: using \: (1))$

$\sf \:  ⟼\dfrac{1}{c} = \dfrac{1}{2} - \dfrac{1}{4}$

$\sf \:  ⟼\dfrac{1}{c} = \dfrac{1}{2} \sf \:  ⟼ \: (3)$

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☆ On substituting (3) in (2), we get

$\sf \:  ⟼\dfrac{1}{b} + \dfrac{1}{4} = \dfrac{1}{3}$

$\sf \:  ⟼\dfrac{1}{b} = \dfrac{1}{3} - \dfrac{1}{4}$

$\sf \:  ⟼\dfrac{1}{b} = \dfrac{4 - 3}{12} = \dfrac{1}{12}$

$\bf\implies \:b \: = \: 12 \: hours$

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☆ Hence, time taken by B to complete the work alone is 12 hours.

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