Question

A can do a piece of work in 14 days which B can do in 21 days. They begin together and work at it for 7 days. Then, A fell ill and B had to complete the work. In how many days, the work was completed?

Answer 1

A can do in $14$ days

In $1$ day A can do $\frac{1}{14}th$ work

B an do in $21$ days

In $1$ day B can do $\frac{1}{21}th$ work

In $7$ days they both do $\frac{7}{14}+\frac{7}{21}th$ of work

$\frac{5}{6}th$ of work

B can do $1$ work in $21$ says

$\frac{1}{6}th$ work in $\frac{21}{6}$ days

$=\frac{7}{2}=3.5$ days

Total no. of days $=7+3.5=10.5$days