If A’s income is 40% of B’s income and B’s income is 24% more than C’s income, then by what percentage is C’s income more than A’s income? (Your answer should be correct to one decimal place.)

Options

A. `75.6`
B. ` 101.6 `
C. `104.2`
D. `50.4`

Answer

To solve the problem step by step, let's denote the incomes of A, B, and C as follows:

1. Let C's income be \( C \).
2. Since B's income is 24% more than C's income, we can express B's income as:
\[ B = C + 0.24C = 1.24C \]

3. According to the problem, A's income is 40% of B's income. Therefore, we can express A's income as:
\[ A = 0.40B \]
Substituting the expression for B from step 2, we have:
\[ A = 0.40 \times 1.24C = 0.496C \]

4. Now, we need to find out by what percentage C's income is more than A's income. The difference between C's income and A's income is:
\[ C - A = C - 0.496C = 0.504C \]

5. To find the percentage by which C's income is more than A's income, we use the formula:
\[ \text{Percentage} = \left( \frac{C - A}{A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{0.504C}{0.496C} \right) \times 100 \]

6. The \( C \) cancels out, so we simplify:
\[ \text{Percentage} = \left( \frac{0.504}{0.496} \right) \times 100 \]

7. Calculating the fraction:
\[ \frac{0.504}{0.496} \approx 1.01613 \]

8. Now, multiplying by 100 gives:
\[ \text{Percentage} \approx 101.613 \]

9. Rounding to one decimal place, we find:
\[ \text{Percentage} \approx 101.6\% \]

Thus, C's income is approximately **101.6%** more than A's income.