Question

Two workers A and B working together completed a job in $5$ days. If A worked twice as efficiently as he actually did and B worked $\frac{1}{3}$ as efficiently as he actually did the work would have been completed in $3$ days. A alone could complete the work in

• A. $5\frac{1}{4}$ days
• B. $6\frac{1}{4}$ days
• C. $7\frac{1}{2}$ days
• D. None of these

Answer 1

Answer: (B)

$6\frac{1}{4}$ days

Let the total work be $W$.
Let the speed of $A$ be $x$ work/day.
Let the speed of $B$ be $y$ work/day.
Two workers $A$ and $B$ working together completed a job in $5$ days.
$\therefore \frac{W}{x+y}=5$$\therefore W=5x+5y$ ..........(1)
If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did the work would have been completed in $3$ day.
$\therefore \frac{W}{2x+\frac{1}{3}y}=3$
$\therefore 5W=30x+5y$ .........(2)
Solving (1) and (2), we get
$\frac{W}{x}=\frac{25}{4}$
$\therefore$ $A$ alone could complete the work in $\frac{25}{4}=6\frac{1}{4}$ days.