Question

A, b and c can do a piece of work in 15 days, b can do it in 30 days and c can do it in 40 days. In how many days will a do the work

Answer 1

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$given \\ (a + b + c) \: can \: do \: a \: peice \: of \: work \: in \: = \: 15 \: days \\ (a + b + c) \: 1 \: day \: work \: = \frac{1}{15} \\ b \: alone \: can \: do \: a \: piece \: of \: work \: in \: = \: 30 \: days \\ b \: 1 \: day \: work \: = \frac{1}{30} \\ c \: alone \: can \: do \: a \: piece \: of \: work \: in = 40 \: days \\ so \\ a \: 1 \: day \: work \: = \frac{1}{15} - \frac{1}{30} + \frac{1}{40} \\ = \frac{1}{15} - \frac{ - 7}{120} \\ = \frac{8 - 1}{120} \\ = \frac{1}{120} \\ therefore \: a \: can \: do \: a \: pieace \: of \: work \: in \: 120 \: days$

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Answer 2

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$given \\ (a + b + c) \: can \: do \: a \: peice \: of \: work \: in \: = \: 15 \: days \\ (a + b + c) \: 1 \: day \: work \: = \frac{1}{15} \\ b \: alone \: can \: do \: a \: piece \: of \: work \: in \: = \: 30 \: days \\ b \: 1 \: day \: work \: = \frac{1}{30} \\ c \: alone \: can \: do \: a \: piece \: of \: work \: in = 40 \: days \\ so \\ a \: 1 \: day \: work \: = \frac{1}{15} - \frac{1}{30} + \frac{1}{40} \\ = \frac{1}{15} - \frac{ - 7}{120} \\ = \frac{8 - 1}{120} \\ = \frac{1}{120} \\ therefore \: a \: can \: do \: a \: pieace \: of \: work \: in \: 120 \: days$

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