Question

A can do a job in 10 days and B in 20 days. They work together, but 4 days before the finish of the job A left. How many days they work together?

• A. $6$
• B. $\frac{16}{3}$
• C. $8$
• D. $14$

Answer 1

The correct option is B $\frac{16}{3}$

Part of work done by $A$ in $1$ day=$\frac{1}{10}$

Part of work done by $B$ in $1$ day=$\frac{1}{20}$

$\because B$ alone worked during last $4$ days.

$\therefore$ part of work done by $B$ in $4$ days=$\frac{4}{20}=\frac{1}{5}$

part of work done by $A$ and $B$(before $4$ days of complete work) =$1-\frac{1}{5}=\frac{5-1}{5}=\frac{4}{5}$

part of work done by $A$ and $B$ in $1$ day= $\frac{1}{10}+\frac{1}{20}=\frac{2+1}{20}=\frac{3}{20}$

$\frac{3}{20}$ part of work done by $A$ and $B$ in $1$ day.

$1$ part of work done by $A$ and $B$ in $\frac{1}{\frac{3}{20}}$ day =$\frac{20}{3}$days.

$\therefore \frac{4}{5}$ part of work is done by $A$ and $B$ in $\frac{20}{3}\times \frac{4}{5}$ days

$=\frac{16}{3}$ days

$5\frac{1}{3}$ days.