Question

 A and B working together can do a piece of work in 12 days . B alone can do the piece of work in 20 days . How long will A takes to do the same work ? [Step 1] find (A and B)' one day work [step 2] B' s one day work [ step 3 ] A's one day work [Step 4] find in how many days A alone can finish the work. ​

Answer 1

Answer:

Step-by-step explanation:

Both A and B can complete 1/12th work in one day

So A+B=1/12 in one day

A alone can complete 1/20 th work

A=1/20 in one day

Now B alone how much work can complete

(1/20)+B=1/12

B =(1/12)-(1/20)

L.C.M of 12 and 20 is 60

So B=( (5–3)/60)

B=2/60=1/30

So alone can complete 1/30th work in one day

B alone can complete the work in 30 days

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• A + B can complete the work in 12 days
• B alone can do the work in 20 days

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• A alone will do the work in = ???

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{One\: day\: work = \dfrac{1}{Total\: time\: taken}}}}}$

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Let the total time taken by A be x

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One day work of ( A+ B ) = $\sf{\bold{\dfrac{1}{12}}}$

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One day work of B = $\sf{\bold{\dfrac{1}{20}}}$

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One day work of A = $\sf{\bold{\dfrac{1}{x}}}$

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We know that ;

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$\sf :\implies\:{\bold{\dfrac{1}{20} = \dfrac{1}{12} +\dfrac{1}{x} }}$

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$\sf :\implies\:{\bold{\dfrac{1}{x} = \dfrac{1}{12} -\dfrac{1}{20} }}$

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$\sf :\implies\:{\bold{\dfrac{1}{x} = \dfrac{5 - 3 }{60} }}$

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$\sf :\implies\:{\bold{\dfrac{1}{x} = \dfrac{2}{60} }}$

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$\sf :\implies\:{\bold{\dfrac{1}{x} = \dfrac{1}{30} }}$

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$\sf :\implies\:{\bold{x = 30 }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• A alone will complete the work in 30 days