A is thrice as good as a workman as $B$ and therefore is able to finish a job in $60$ days less than $B$. How much time will they take to finish the same job if they work together?
My attempt:
Let's say that the amount of work done by $B$ in $1$ day = $1 \over B$
As $A$ is $3$ times better than $B$, hence the amount of work done by $A$ in $1$ day=$3 \over B$
The difference in times to complete the same work is $60$ days.
Hence, ${3 \over B} - {1 \over B} = {1 \over 60}$
Solving which gives me B as 120 days and A as 40 days. Working together, they can complete the same job in ${ 1 \over {1 \over 120} + {1 \over 40}}= 30$ days.
But the correct answer, as given in the question, is something else.
What did I do wrong?