Question

A works half of B's ​​3/4 of the time. If A and B work together in 18 days, then B alone will work in how many days?​

Answer 1

$\huge \mathbb \red{ANSWER}$

$\bf{ \boxed{ \underline{ \blue{ \tt{x = 30 \: }}}}}$

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$\sf \huge \underline \pink{Question}$

A works half of B's 3/4 of the time. If A and B work together in 18 days, then B alone will work in how many days?

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$\sf \ \underline \pink{step \: by \: step \: explanation}$

$\rm \blue{➷ \: let \: b \: work \: complete \: be \: x}$

$\rm \green{➷ \: time \: taken \: by \: a \: will \: be \: \frac{1}{2} \: will \: be \: \frac{3}{4}}$

$\rm \green{ = \frac{3x}{4}}$

$\bf \red{time \: taken \: by \: a \: will \: be \: \frac{3x}{4} \times 2 = \frac{3x}{2}}$

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$\bf{ \underline{ \underline{ \pink{Now \: }}}}$

$\tt \orange{➷ \: A \: day \: work = \frac{2}{3x}}$

$\tt \purple{➷ \: B \: work \: = \frac{1}{x}}$

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

if a and b work together in 18 days

$\tt \underline{➷ \: so \: a \: and \: b \: work \: be \: \frac{1}{18}}$

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According to question..

$\bf \blue{➷ \: \frac{2}{3x} + \frac{1}{x} = \frac{1}{18}}$

$\bf \red{➷ \: x = 30}$

so,

B days take 30 days to work

$\bf{ \boxed{ \underline{ \pink{ \tt{x = 30 \: }}}}}$