If X is 30% less than Y and Z is 50% less than Y, then Z is how much percentage less than Y?

Options

A. `80%`
B. `95%`
C. `65%`
D. `75%`

Answer

To solve the problem step by step, we need to find out how much percentage less Z is than Y, given that X is 30% less than Y and Z is 50% less than Y.

### Step 1: Define Y
Let’s assume the value of Y is 100 (this makes calculations easier, but any value can be used).

### Step 2: Calculate X
Since X is 30% less than Y:
\[ X = Y - 30\% \text{ of } Y = Y - 0.30Y = 0.70Y \]
Substituting Y = 100:
\[ X = 0.70 \times 100 = 70 \]

### Step 3: Calculate Z
Since Z is 50% less than Y:
\[ Z = Y - 50\% \text{ of } Y = Y - 0.50Y = 0.50Y \]
Substituting Y = 100:
\[ Z = 0.50 \times 100 = 50 \]

### Step 4: Find the difference between Y and Z
Now we need to find how much less Z is than Y:
\[ \text{Difference} = Y - Z = 100 - 50 = 50 \]

### Step 5: Calculate the percentage difference
To find out how much percentage less Z is than Y, we use the formula:
\[ \text{Percentage less} = \left(\frac{\text{Difference}}{Y}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage less} = \left(\frac{50}{100}\right) \times 100 = 50\% \]

### Conclusion
Thus, Z is 50% less than Y.

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