X, Y and Z can complete a piece of work in 10 days. X and Y can do it in 20 days. Then Z alone can complete the work in ……………… days.

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the work done by X, Y, and Z together.
Given that X, Y, and Z can complete the work in 10 days, we can find their combined work rate.

- Work done by X, Y, and Z in 1 day = 1/10 of the work.

### Step 2: Determine the work done by X and Y together.
It is given that X and Y can complete the work in 20 days.

- Work done by X and Y in 1 day = 1/20 of the work.

### Step 3: Calculate the work done by Z alone.
To find the work done by Z alone, we can use the information from Steps 1 and 2.

- Work done by Z in 1 day = Work done by X, Y, and Z in 1 day - Work done by X and Y in 1 day
- Work done by Z in 1 day = (1/10) - (1/20)

### Step 4: Find a common denominator and simplify.
To perform the subtraction, we need a common denominator.

- The common denominator of 10 and 20 is 20.
- Convert (1/10) to (2/20):

Work done by Z in 1 day = (2/20) - (1/20) = (1/20)

### Step 5: Calculate the time taken by Z to complete the work alone.
If Z can do 1/20 of the work in one day, then the total time taken by Z to complete the entire work is:

- Time taken by Z = Total work / Work done by Z in 1 day
- Time taken by Z = 1 / (1/20) = 20 days

Thus, Z alone can complete the work in **20 days**.

### Final Answer:
Z alone can complete the work in **20 days**.

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