Question

A can do a piece of work In 14 days while 13 can do it In 21 days. They began together and worked at It for 6 days. Then. A fell ill and B had to complete the remaining work alone. In how many days was the work completed?

Answer 1

A's 1 day's work $=\frac{1}{14}$

B's 1 day's work $=\frac{1}{21}$

A and B's 1 day's work $=\frac{1}{14}+\frac{1}{21}=\frac{3+2}{42}=\frac{5}{42}$

A and B's 6 days work $=\frac{5}{42}\times 6=\frac{5}{7}$

Remaining work $=1-\frac{5}{7}=\frac{2}{7}$

B will finish $\frac{2}{7}$ work in $=\frac{2}{7}\times 21=6$ day $\therefore$ The whole work will finish in =6+6=12 days