Question

A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then Joined by B. Find the total time taken to finish the work.

Answer 1

A's one day's work $=\frac{1}{16}$

B's one day's work $=\frac{1}{12}$

A and B's one day's work $=\frac{1}{16}+\frac{1}{12}$

$=\frac{3+4}{48}=\frac{7}{48}$

A's 2 days work $=\frac{1}{16}\times 2=\frac{1}{8}$

Remaining work $=1-\frac{1}{8}=\frac{7}{8}$

$\therefore$ A and B will finish the $\frac{7}{8}$ work in

$=\frac{7}{8}\times \frac{48}{7}=6$ days

$\therefore$ Whole work will be finished in 2+6 =8 days