The income of X is 60% more than Y's income and the income of Y is 40% more than Z's income. X's income is how much percentage more than Z's income?

Options

A. A) 134
B. B) 224
C. C) 100
D. D) 124

Answer

To solve the problem, we need to determine how much more X's income is compared to Z's income in percentage terms. We'll break it down step by step.

### Step 1: Define the incomes
Let:
- Y's income = Y
- Z's income = Z

According to the problem:
- X's income is 60% more than Y's income.
- Y's income is 40% more than Z's income.

### Step 2: Express X's income in terms of Y
Since X's income is 60% more than Y's income, we can express it mathematically as:
\[ X = Y + 0.6Y = 1.6Y \]

### Step 3: Express Y's income in terms of Z
Since Y's income is 40% more than Z's income, we can express it as:
\[ Y = Z + 0.4Z = 1.4Z \]

### Step 4: Substitute Y's income into X's income
Now, we can substitute the expression for Y into the equation for X:
\[ X = 1.6Y = 1.6(1.4Z) \]
Calculating this gives:
\[ X = 1.6 \times 1.4Z = 2.24Z \]

### Step 5: Calculate the percentage increase of X's income over Z's income
To find out how much percentage more X's income is than Z's income, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{X - Z}{Z} \right) \times 100 \]
Substituting X = 2.24Z into the formula:
\[ \text{Percentage Increase} = \left( \frac{2.24Z - Z}{Z} \right) \times 100 \]
This simplifies to:
\[ \text{Percentage Increase} = \left( \frac{1.24Z}{Z} \right) \times 100 = 1.24 \times 100 = 124\% \]

### Conclusion
Thus, X's income is **124%** more than Z's income.