Question

Two worker of varying skills can do a work in $10$ minutes if they work together. If the first worker worked alone for $10$ minutes and the second worker worked alone for $2$ minutes, then they would be left with $\frac{1}{5}$ of the whole work. How many minutes would it take the slower worker to complete the work alone?

• A. $30$ minutes
• B. $40$ minutes
• C. $20$ minutes
• D. $50$ minutes

Answer 1

The correct option is B $40$ minutes

One minute's work of both worker $=\frac{1}{10}$
Let one minutes's work of first worker be $x.$
Then, one minutes's work of second worker $=\frac{1}{10}-x$
According to question,
$10x+2(\frac{1}{10}-x)=\frac{4}{5}$
$\Rightarrow \frac{1}{5}+8x=\frac{4}{5}$
$\Rightarrow 8x=\frac{3}{5}$
$\Rightarrow x=\frac{3}{40}$
So, one minutes's work of second worker $=\frac{1}{10}-\frac{3}{40}=\frac{1}{40}$
Therefore, first worker will take $\frac{40}{3}$ minutes to complete the work alone and second worker will take $40$ minutes to complete the work alone.