X can do 20% of a work in a day, Y can do 25% of the same work in a day and X, Y and Z together can do 50% of the same work in a day. How many per cent of work can be done by Z in a day?

Options

A. 5%
B. 7%
C. 10%
D. 13%

Answer

To find out how much work Z can do in a day, we can follow these steps:

1. **Identify the work done by X and Y**:
- X can do 20% of the work in a day.
- Y can do 25% of the work in a day.

2. **Calculate the total work done by X and Y together**:
- Total work done by X and Y in a day = Work done by X + Work done by Y
- Total work done by X and Y = 20% + 25% = 45%

3. **Use the information about X, Y, and Z together**:
- We know that X, Y, and Z together can do 50% of the work in a day.

4. **Set up the equation**:
- Work done by X + Work done by Y + Work done by Z = 50%
- Substitute the known values: 20% + 25% + Work done by Z = 50%

5. **Solve for the work done by Z**:
- 20% + 25% + Z = 50%
- Combine the known percentages: 45% + Z = 50%
- To find Z, subtract 45% from both sides:
Z = 50% - 45%
Z = 5%

6. **Conclusion**:
- Therefore, Z can do 5% of the work in a day.