Answer:
Y alone can do the piece of work in 30 days.
Step-by-step explanation:
Proportions
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
[tex]\displaystyle \frac{1}{15}+\frac{1}{N}[/tex]
parts of the work per day. We know they can finish it in 10 days, thus:
[tex]\displaystyle \frac{1}{15}+\frac{1}{N}=\frac{1}{10}[/tex]
Rearranging:
[tex]\displaystyle \frac{1}{N}=\frac{1}{10}-\frac{1}{15}[/tex]
The LCM of 10 and 15 is 30, thus operating:
[tex]\displaystyle \frac{1}{N}=\frac{3-2}{30}=\frac{1}{30}[/tex]
Solving for N:
N = 30
Y alone can do the piece of work in 30 days.
