Question

A, B and C working together can finish a piece of work in 8 hours. Aalone can do it in 20 hours and B alone can do it in 24 hours in how many hours will C alone do the same work​

Answer 1

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$In \: 1 \: hour, \: they \: do \: ⅛ \: work.$

$A, alone, \: does \: it \: in \: 20 \: hours.$

$In \: 1 \: hour, \: 1/20 \: of \: the \: work.$

$B, alone, \: finishes \: it \: in \: 24 \: hours.$

$In \: 1 \: hour, \: he \: would \: do \: 1/24 \: of \: the \: work.$

$So, \: total \: work \: done \: by \: A \: and \: B \: in \: 1 \: hour$

$= 1/20 + 1/24 = 6 + 5/ 120 = 11/120 \: of \: the \: work.$

$Hence, \: C’s \: 1 \: hour \: work = 1/8 - 11/120 = (15-11)/120$

$= 4/120 = 1/30 \: of \: the \: work.$

$1/30 \: work \: of \: the \: work \: is \: done \: in \: 1 \: hour \: by \: C$

$1 \: whole \: work \: would \: be \: done \: in \: 1/(1/30) = 30 hours \: by \: C.$