A can do a piece of work in 80 days. He works at it for 10 days and th

1.	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 many days can the two of them complete the work together ?
Answer» A’s 1 days’ work = \(\frac{1}{80}\) A’s 10 days’ work = \(\frac{10}{80}\) = \(\frac{1}{8}\) Remaining work = 1 - \(\frac{1}{8}\) = \(\frac{7}{8}\) \(\frac{7}{8}\) of the work is completed by B in 42 days. \(\therefore\) The whole work is completed by B in \(\frac{42\times8}{7}\) days = 48 days \(\therefore\) B’s 1 days’ work = \(\frac{1}{48}\) (A + B)’s 1 days’ work = \(\frac{1}{80}\) + \(\frac{1}{48}\) = \(\frac{3+5}{240}\) = \(\frac{8}{240}\) = \(\frac{1}{30}\) \(\therefore\) A and B can complete the whole work together in 30 days.

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 many days can the two of them complete the work together ?

Answer»

A’s 1 days’ work = \(\frac{1}{80}\)

A’s 10 days’ work = \(\frac{10}{80}\) = \(\frac{1}{8}\)

Remaining work = 1 - \(\frac{1}{8}\) = \(\frac{7}{8}\)

\(\frac{7}{8}\) of the work is completed by B in 42 days.

\(\therefore\) The whole work is completed by B in \(\frac{42\times8}{7}\) days = 48 days

\(\therefore\) B’s 1 days’ work = \(\frac{1}{48}\)

(A + B)’s 1 days’ work = \(\frac{1}{80}\) + \(\frac{1}{48}\) = \(\frac{3+5}{240}\) = \(\frac{8}{240}\) = \(\frac{1}{30}\)

\(\therefore\) A and B can complete the whole work together in 30 days.