Initially B works alone for five days then C joins and after three mor

1.	Initially B works alone for five days then C joins and after three more days A joins and B leaves, in how many was the work completed?1). \(30\frac{{14}}{{39}}\) days2). \(36\frac{{19}}{{39}}\) days3). \(33\frac{{20}}{{39}}\) days4). \(34\frac{{21}}{{39}}\) days
Answer» Initially B works alone for FIVE DAYS B’s one day work = $(\frac{1}{{60}})$ ∴ Work done $(= 5 \times \;\frac{1}{{60}} = \frac{1}{{12}})$ ∴ Work left $(= 1 - \frac{1}{{12}} = \frac{{11}}{{12}})$ C joins and B and C work for three days C’s one day work = $(\frac{1}{{80}})$ B and C’s one day work = $(\frac{1}{{60}} + \;\frac{1}{{80}} = \;\frac{7}{{240}})$ ∴ Work done $(= 3 \times \frac{7}{{240}} = \frac{7}{{80}})$ ∴ Work left $(= \frac{{11}}{{12}} - \frac{7}{{80}} = \frac{{199}}{{240}})$ After three more days A joins and B leaves, A and C work together A and C’s one day work = $(\frac{1}{{50}} + \frac{1}{{80}} = \frac{{13}}{{400}})$ Work left = $(\frac{{199}}{{240}})$ ∴ Days TAKEN to complete the remaining work $(= \frac{{199}}{{240}} \times \frac{{400}}{{13}} = \frac{{995}}{{39}})$ ∴ Total number of days $(= 5 + 3 + \;\frac{{995}}{{39}} = 33\frac{{20}}{{39}})$ days

Initially B works alone for five days then C joins and after three more days A joins and B leaves, in how many was the work completed?1). $30\frac{{14}}{{39}}$ days2). $36\frac{{19}}{{39}}$ days3). $33\frac{{20}}{{39}}$ days4). $34\frac{{21}}{{39}}$ days

Answer»

Initially B works alone for FIVE DAYS

B’s one day work = $(\frac{1}{{60}})$

∴ Work done $(= 5 \times \;\frac{1}{{60}} = \frac{1}{{12}})$

∴ Work left $(= 1 - \frac{1}{{12}} = \frac{{11}}{{12}})$

C joins and B and C work for three days

C’s one day work = $(\frac{1}{{80}})$

B and C’s one day work = $(\frac{1}{{60}} + \;\frac{1}{{80}} = \;\frac{7}{{240}})$

∴ Work done $(= 3 \times \frac{7}{{240}} = \frac{7}{{80}})$

∴ Work left $(= \frac{{11}}{{12}} - \frac{7}{{80}} = \frac{{199}}{{240}})$

After three more days A joins and B leaves, A and C work together

A and C’s one day work = $(\frac{1}{{50}} + \frac{1}{{80}} = \frac{{13}}{{400}})$

Work left = $(\frac{{199}}{{240}})$

∴ Days TAKEN to complete the remaining work $(= \frac{{199}}{{240}} \times \frac{{400}}{{13}} = \frac{{995}}{{39}})$

∴ Total number of days $(= 5 + 3 + \;\frac{{995}}{{39}} = 33\frac{{20}}{{39}})$ days