Question

A and B together can do a peice of work in 10 days,but A alone can do it in 15 days .how much time would B alone take to do the same work?​

Answer 1

$\huge\underline\mathrm{Question-}$

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A and B together can do a piece of work in 10 days, but A alone can do it in 15 days. How much time would B alone take to do the same work?

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$\huge\underline\mathrm{Answer-}$

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B alone can complete this piece of work in 30 days.

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$\huge\underline\mathrm{Explanation-}$

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It is given that A and B together can do a piece of work in 10 days.

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$\therefore$ A and B can together do $\dfrac{1}{10}$ of work in 1 day.

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$\mapsto$ Work of A + Work of B = $\dfrac{1}{10}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (1)

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It is also given that A alone can do same piece of work in 15 days.

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$\therefore$ A can do $\dfrac{1}{15}$ of work in 1 days.

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$\mapsto$ Work of A = $\dfrac{1}{15}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (2)

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★ Put the value of eq (2) in (1).

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$\mapsto$ $\dfrac{1}{15}$ + Work of B = $\dfrac{1}{10}$

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$\mapsto$ Work of B = $\dfrac{1}{10}\:-\:\dfrac{1}{15}$

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$\mapsto$ Work of B = $\dfrac{3-2}{30}$

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$\mapsto$ Work of B = $\dfrac{1}{30}$

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So, B can do $\dfrac{1}{30}$ of total work in 1 day.

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Hence, B can alone do a piece of work in 30 days.

Answer 2

Answer:

${\boxed{\tt{B\:alone\:can\:do\:in\: \: 30\:days.}}}$

Step-by-step explanation:

Given that:-

• A and B together can do the work in 10 days.
• A alone can do it in 15 days.
• B alone can do the work in = ? days.

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$\tt A \: and \:B \: can \: do \: it \: in 10\:days. \\\therefore\tt They\:both\:can\:do\:in\: <strong>1</strong><strong> </strong>day = \frac{1}{10}\:of\: work$

$\tt A \:alone\:can\:do\:it \: in \: 15\:days.\\\therefore\tt A\:alone \:can\:do \: in\: <strong>1</strong><strong> </strong>day = \frac{1}{15}\:of\:work.$

${\underline{\underline{\tt{According\:to\:question:}}}}$

$\rightarrow\tt \frac{1}{15} + \frac{1}{B} =\frac{1}{10} \\\rightarrow\tt \frac{1}{B} = \frac{1}{10} - \frac{1}{15} \\\rightarrow\tt \frac{1}{B} = \frac{3-2}{30} \\\rightarrow\tt \frac{1}{B} = \frac{1}{30} \\\rightarrow{\boxed{\tt{B\:alone\:can\:do\:in=30\:days.}}}$

$\therefore\bold{\underline{B\:alone\:can\:do\:the\:work\:in=30\:days.}}$