If A’s income is `25%` more than B’s income and B’s income is `20%` more than C’s by what percent is A’s income more than C’s?

Options

A. A)`15%`
B. B)`25%`
C. C)`33%`
D. D)`50%`

Answer

To solve the problem step-by-step, we need to express the incomes of A, B, and C in terms of a common variable and then find the percentage difference between A's income and C's income.

### Step 1: Define B's Income
Let B's income be represented as \( B \).

### Step 2: Calculate A's Income
According to the problem, A's income is 25% more than B's income. This can be calculated as:
\[ A = B + 0.25B = 1.25B \]

### Step 3: Calculate C's Income
B's income is also stated to be 20% more than C's income. Thus, we can express C's income as:
\[ B = C + 0.20C = 1.20C \]
From this, we can express C's income in terms of B's income:
\[ C = \frac{B}{1.20} = \frac{B}{\frac{6}{5}} = \frac{5B}{6} \]

### Step 4: Express A's Income in Terms of C's Income
Now we have:
- \( A = 1.25B \)
- \( C = \frac{5B}{6} \)

We can substitute C's income into the equation for A's income:
\[ A = 1.25B = 1.25 \times \left( \frac{6C}{5} \right) = \frac{1.25 \times 6C}{5} = \frac{7.5C}{5} = 1.5C \]

### Step 5: Calculate the Percentage Increase of A's Income over C's Income
To find out by what percent A's income is more than C's income, we can use the formula:
\[ \text{Percentage Increase} = \left( \frac{A - C}{C} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{1.5C - C}{C} \right) \times 100 = \left( \frac{0.5C}{C} \right) \times 100 = 0.5 \times 100 = 50\% \]

### Final Answer
A's income is 50% more than C's income.

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