$A$ is $4$ times as good as $K$ and hence, $K$ takes $50$ more days than $A$ to complete a job. How long will it take to finish the job if they work together?
I tried and got:
$A=6$%/day
$K=1.5$%/day
$A+K=7.5$%/day therefore $13.\overline{3}$ days in all.
But the book has answer $20$ days. What's wrong?
To answer your final question: the book is.
I get the same as you. It's easy to see that even A alone will finish in less than $20$ days, since if A took $20$ and K took $70$, A would only be $3.5$ times as fast as K, and this ratio gets lower as you increase the times.
I'm not sure exactly what mistake has been made in the book. The easiest way to make it work would be to change $50$ to $75$, and then the numbers work out quite nicely with an exact number of days at every stage.
