Question

A can build a wall in $25$ days and $B$ can demolish the same wall in $80$ days and $C$ can build the same wall in $60$ days. If they work on consecutive day one after another starting from $A$ on the first day. Then in how many days will the work be completed?

• A. $67\frac{49}{53}days$
• B. $67\frac{17}{24}days$
• C. $66\frac{17}{24}days$
• D. $68\frac{17}{24}days$

Answer 1

The correct option is A $67\frac{49}{53}days$

$A$ can build wall in $25$ days

$A^{\prime }s$ one day work $=\frac{1}{25}$

$B$ can demolish wall in $80$ days

$B^{\prime }s$ one day work $=\frac{-1}{80}$

$C$ can build wall in $60$ days

$C^{\prime }s$ one day work $=\frac{1}{60}$

$A,B,C$ work together $=\frac{1}{25}-\frac{1}{80}-\frac{1}{60}$

$=\frac{48-15+20}{1200}=\frac{53}{1200}$

Fraction of wall built in $3$ days $=\frac{53}{1200}$

Fraction of wall build in $1$ days $=\frac{53}{1200}\times \frac{1}{3}$

$\therefore$ Total no. of days $=\frac{3600}{53}=67\frac{49}{53}$ days.