If initially C and D work together for eight days and after that A joi

1.	If initially C and D work together for eight days and after that A joins them, they all work four days, after which B joins and c leaves, in how many total days was the assignment completed?1). \(25\frac{{10}}{{13}}\) days2). \(29\frac{9}{{13}}\) days3). \(24\frac{{11}}{{13}}\) days4). \(27\frac{{12}}{{13}}\) days
Answer» Initially C and D work together for eight DAYS C’s one day work = $(\frac{1}{{80}})$ D’s one day work = $(\frac{1}{{150}})$ C and D’s one day work $(= \frac{1}{{80}} + \frac{1}{{150}} = \frac{{23}}{{1200}})$ ∴ Work done $(= 8 \times \frac{{23}}{{1200}} = \frac{{23}}{{150}})$ ∴ Work left $(= 1 - \frac{{23}}{{150}} = \frac{{127}}{{150}})$ After that A joins them, they all work four days, A, C and D’s one day work $(= \frac{1}{{50}} + \frac{1}{{80}} + \frac{1}{{150}} = \frac{{47}}{{1200}})$ Work done $(= 4 \times \frac{{47}}{{1200}} = \frac{{47}}{{300}})$ Work left $(= \frac{{127}}{{150}} - \frac{{47}}{{300}} = \frac{{69}}{{100}})$ After which B joins and C LEAVES, in how MANY total days was the assignment completed A, B and D’s one day work $(= \frac{1}{{50}} + \frac{1}{{60}} + \frac{1}{{150}} = \frac{{13}}{{300}})$ Work left $(= \frac{{69}}{{100}})$ ∴ Days taken to complete the REMAINING work $(= \frac{{69}}{{100}} \times \frac{{300}}{{13}} = \frac{{207}}{{13}})$ ∴ Total days taken $(= 8 + 4 + \;\frac{{207}}{{13}} = 27\frac{{12}}{{13}})$ days

If initially C and D work together for eight days and after that A joins them, they all work four days, after which B joins and c leaves, in how many total days was the assignment completed?1). $25\frac{{10}}{{13}}$ days2). $29\frac{9}{{13}}$ days3). $24\frac{{11}}{{13}}$ days4). $27\frac{{12}}{{13}}$ days

Answer»

Initially C and D work together for eight DAYS

C’s one day work = $(\frac{1}{{80}})$

D’s one day work = $(\frac{1}{{150}})$

C and D’s one day work $(= \frac{1}{{80}} + \frac{1}{{150}} = \frac{{23}}{{1200}})$

∴ Work done $(= 8 \times \frac{{23}}{{1200}} = \frac{{23}}{{150}})$

∴ Work left $(= 1 - \frac{{23}}{{150}} = \frac{{127}}{{150}})$

After that A joins them, they all work four days,

A, C and D’s one day work $(= \frac{1}{{50}} + \frac{1}{{80}} + \frac{1}{{150}} = \frac{{47}}{{1200}})$

Work done $(= 4 \times \frac{{47}}{{1200}} = \frac{{47}}{{300}})$

Work left $(= \frac{{127}}{{150}} - \frac{{47}}{{300}} = \frac{{69}}{{100}})$

After which B joins and C LEAVES, in how MANY total days was the assignment completed

A, B and D’s one day work $(= \frac{1}{{50}} + \frac{1}{{60}} + \frac{1}{{150}} = \frac{{13}}{{300}})$

Work left $(= \frac{{69}}{{100}})$

∴ Days taken to complete the REMAINING work $(= \frac{{69}}{{100}} \times \frac{{300}}{{13}} = \frac{{207}}{{13}})$

∴ Total days taken $(= 8 + 4 + \;\frac{{207}}{{13}} = 27\frac{{12}}{{13}})$ days