Question

$A$ does half as much work as $B$ and $C$ does half as much work as $A$ and $B$ together in the same time. If $C$ alone can do the work in $40$ days, all of them together will finish the work in

• A. $13$ days
• B. $15$ days
• C. $20$ days
• D. $13.33$ days

Answer 1

Answer: (D)

$13.33$ days

$Letthetotalworkbexunits.$
$\therefore speedofCis=\frac{x}{40}workperday.$
$\therefore SpeedofB=\frac{x}{30}worksperday.$
$\therefore SpeedofA=\frac{x}{60}worksperday.$
$\therefore SpeedofA+B+C=\frac{3x}{40}worksperday.$
$Ifallofthemworktogetherthentheywillfinishxworksin\frac{x}{\frac{3x}{40}}=13.33days.$