Question

Two typist of varying skills can do a job in $6$ minutes if they work together. If the first typist typed alone for $4$ minutes and then the second typist typed alone for $6$ minutes, then they would be left with $\frac{1}{5}$ of the whole work. How many minutes would it take the slower typist to complete the typing job working alone?

• A. $10$ minutes
• B. $15$ minutes
• C. $12$ minutes
• D. $20$ minutes

Answer 1

The correct option is B $15$ minutes

One minute's work of both typists $=\frac{1}{6}$
Let one minutes's work of first typist be $x$
Then, one minutes's work of second typist $=\frac{1}{6}-x$
According to question,
$4x+6(\frac{1}{6}-x)=\frac{4}{5}$
$\Rightarrow 2x=\frac{1}{5}$
$\Rightarrow x=\frac{1}{10}$
So, second typist one minute's work $=\frac{1}{6}-\frac{1}{10}=\frac{1}{15}$
Therefore, first typist will take $10$ minutes to complete the typing job alone and second typist will take $15$ minutes to complete the typing job alone.