Question

A can do a piece of work in 10 days and B can do it in 15 days. How long will they take to complete it together?​

Answer 1

Answer:

6 days

Step-by-step explanation:

A took 10 days for full work.

A will finish 1/10th of the work in 1 day.

B took 15 days for full work.

B will finish 1/15th of work in 1 day.

In 1 day ,

A and B together will complete = 1/10 + 1/15 of the work= 1/6 of the work

Thus. they will take 6 days together...

Answer 2

Given:-

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• A can do the work in 10 days
• B can do the work in 15 days

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To Find :-

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• How long will they to complete the work together

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Solution :-

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

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$\sf:\implies \: {\bold{ A's\:one\: day: work\: = \: \dfrac{1}{10} }}$

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$\sf:\implies \: {\bold{ B's\:one\: day: work\: = \: \dfrac{1}{15} }}$

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$\sf:\implies \: {\bold{ ( A + B )'s \:one\: day: work\: = \: \dfrac{1}{10} + \dfrac{1}{15} }}$

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$\sf:\implies \: {\bold{ ( A + B )'s \:one\: day: work\: = \: \dfrac{3 + 2 }{30} }}$

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$\sf:\implies \: {\bold{ ( A + B )'s \:one\: day: work\: = \: \dfrac{5}{30}}}$

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$\sf:\implies \: {\bold{ ( A + B )'s \:one\: day: work\: = \: \dfrac{1}{6} }}$

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

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$\sf:\implies \: {\bold{ \dfrac{1}{6} = \dfrac{1}{Total\: time} }}$

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$\sf:\implies \: {\bold{Total\: time = \dfrac{1}{\dfrac{1}{6}} }}$

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$\sf:\implies \: {\bold{ Total\: time = 6days }}$

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Answer :-

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• A and B will together complete their work in 6 days

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