Question

A can do a piece of work in $80days$.He work at it for $10$ days and then $B$ alone finishes the work in $42$ day.In how much time will A and B working together,finish the work?

• A. $30$ days
• B. $25$ days
• C. $20$ days
• D. $35$ days

Answer 1

The correct option is A $30$ days

A can complete a work in $80$ days

A can work in one day$=\frac{1}{80}$

then,

A leave the work after $10$ days

$=\frac{1}{80}\times 10$

$=\frac{1}{8}$

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

$=\frac{7}{8}$

B complete remaining work$=42$ days

$\frac{7}{8}=42$

B can complete whole work in

$=\frac{42\times 3}{7}$

$=48$

B can work in one day$=\frac{1}{48}$

A and B can complete the work together$=\frac{1}{80}+\frac{1}{48}$

$=\frac{3+5}{240}$

$=\frac{8}{240}$

$=\frac{1}{30}$

$30$ days.