Answer:
<em>Y alone can do the piece of work in 30 days.</em>
Step-by-step explanation:
<u>Proportions</u>
Let's make:
N = days for Y to finish the work alone
Since X alone can do it in 15 days, each day he can do a proportion of 1/15 of the piece of work.
Since Y alone can (possibly) do it in N days, each day he can do 1/N parts of the work.
Together, they do
parts of the work per day. We know they can finish it in 10 days, thus:
Rearranging:
The LCM of 10 and 15 is 30, thus operating:
Solving for N:
N = 30
Y alone can do the piece of work in 30 days.