Question

A can do a piece of work in 14 days which B can DO IN 21DAYS .THEY BEGIN TOGETHER BUT 3 DAYS BEFORE TEH COMPLETION OF WORK A LEAVES OFF. THE TOTAL NUMBER OF DAYS TO COMPLETE THE WORK IS WHAT

Answer 1

$A's 1 day work = \frac{1}{14} \\ B's 1day work= \frac{1}{21} \\ A+B \: 3 \: day work = (\frac{1}{14} + \frac{1}{21} ) \times 3\\ = (\frac{3 + 2}{42} ) \times 3 \\ = \frac{5}{42} \times 3\\ remaining \: work \: = \frac{15}{42} \\ B \: can \: do \: this \: work \: in = \frac{15}{42} \div \frac{1}{21} = 7.5 \: days$