Question

$A,B$ and $C$ complete a piece of work in $25,20$ and $24$ days respectively. All work together for $2$ days and then $A$ and $B$ leave the work . $C$ works for next $8\frac{3}{5}$ days and then $A$ along with $D$ join $C$ and they all finish the work in next three days. In how many days $D$ alone can complete the whole work ?

• A. $22$ days
• B. $21\frac{1}{2}$days
• C. $23$ days
• D. $22\frac{1}{2}$days

Answer 1

Answer: (D)

$22\frac{1}{2}$days

Let the amount of work be $x$.

Now $A$ does the work in $25$ days.

$\therefore$ In $1$ day $A$ does $\frac{x}{25}$ work,

$B$ does the work in $20$ days.

$\therefore$ In $1$ day $B$ does $\frac{x}{20}$ work,

$C$ does the work in $24$ days.

$\therefore$ In $1$ day $C$ does $\frac{x}{24}$ work.

$A$ works for $(2+3)$ days $=5$ days.

$\therefore$ In $5$ days $A$ does $5\times \frac{x}{25}$ work $=$ $\frac{x}{5}$ work,

$B$ works for $2$ days.

$\therefore$ In $5$ days $B$ does $2\times \frac{x}{20}$ work=$\frac{x}{10}$ and

$C$ works for $(2+8\frac{3}{5}+3)$days=$\frac{68}{5}$days.

$\therefore$ In $\frac{68}{5}$ days $C$ does $\frac{68}{5}\times \frac{x}{24}$ work=$\frac{17x}{15}$ work.

$\therefore$ The total work done by $A,B$ and $C$, so far $=$ $\frac{x}{5}+\frac{x}{10}+\frac{17x}{13}$ work $=$ $\frac{13x}{15}$ work.

$\therefore$ The work left $=$ $x-\frac{13x}{15}$ work

This work is done by $D$ in $3$ days.

$\therefore$ $D$ will finish the whole i.e $x$ work in $3\times \frac{15}{2}$days $=$$22\frac{1}{2}$ days.

Ans- Option D.