InterviewSolution
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A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?1). 30 days2). 32 days3). 26 days4). 27 days |
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Answer» A can do a PIECE of WORK in 80 days. $(\begin{array}{l} {\rm{Work\;done\;by\;A\;in\;}}1{\rm{\;days}} = \frac{1}{{80}}\\ {\rm{Work\;done\;by\;A\;in\;}}10{\rm{\;days}} = \frac{1}{{80}}{\rm{\;}} \times 10 = \frac{1}{8}\\ \THEREFORE {\rm{Remaining\;work\;to\;be\;done\;by\;B}} = 1 - \frac{1}{8} = \frac{7}{8}\\ \frac{7}{8}{\rm{\;of\;the\;work\;is\;done\;by\;B\;in\;}}42{\rm{\;days\;}}\\ \therefore {\rm{Complete\;work\;is\;done\;by\;B\;in}} = 42{\rm{\;}} \times \frac{8}{7} = 6 \times 8 = 48{\rm{\;days\;}}\\ {\rm{Work\;done\;by\;A\;in\;}}1{\rm{\;day}} = \frac{1}{{80}}{\rm{\;and\;work\;done\;by\;B\;in\;}}1{\rm{\;day}} = \frac{1}{{48}}\\ \therefore {\rm{A\;and\;B's\;}}1{\rm{\;day's\;work}} = \frac{1}{{80}} + \frac{1}{{48}} = \frac{8}{{240}} = \frac{1}{{30}} \end{array})$ ∴ Both will finish the work in 30 days. |
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