Question : X alone can finish a work in 18 days, and Y alone can finish the same work in 9 days. If X, Y, and Z together can finish the same work in 4 days, then in how many days Z alone can finish the work?
Option 1: 12 days
Option 2: 10 days
Option 3: 14 days
Option 4: 16 days
Correct Answer: 12 days
Solution :
Let the rate at which X, Y, and Z can finish the work as $R_x, R_y$ and $R_z$, respectively.
Given that X can finish the work in 18 days.
⇒ $R_x=\frac{1}{18}$ work per day
Given that Y can finish the work in 9 days.
⇒ $R_y=\frac{1}{9}$ work per day
Given that X, Y, and Z together can finish the work in 4 days.
⇒ $R_x + R_y + R_z=\frac{1}{4}$ work per day
⇒ $R_z=(R_x + R_y + R_z) -R_x - R_y=\frac{1}{4}-\frac{1}{18}-\frac{1}{9}=\frac{1}{12}$ work per day
So, Z alone can finish the work in 12 days.
Hence, the correct answer is 12 days.
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