A is `20%` more than B which is `30%` more than C which is `10%` more than D. by what percent is A more than D?

Options

A. A)`71.6%`
B. B)`6%`
C. C)`90.67%`
D. D)`82.5%`

Answer

To solve the problem step by step, we will first define the relationships between A, B, C, and D based on the percentages given in the question.

### Step 1: Define the values
Let the value of D be \( D = 100 \) (we can use any base value, but 100 makes percentage calculations easier).

### Step 2: Calculate C
Since C is 10% more than D:
\[ C = D + 10\% \text{ of } D = 100 + 10\% \text{ of } 100 = 100 + 10 = 110 \]

### Step 3: Calculate B
B is 30% more than C:
\[ B = C + 30\% \text{ of } C = 110 + 30\% \text{ of } 110 = 110 + 33 = 143 \]

### Step 4: Calculate A
A is 20% more than B:
\[ A = B + 20\% \text{ of } B = 143 + 20\% \text{ of } 143 = 143 + 28.6 = 171.6 \]

### Step 5: Calculate the difference between A and D
Now we find the difference between A and D:
\[ \text{Difference} = A - D = 171.6 - 100 = 71.6 \]

### Step 6: Calculate the percentage by which A is more than D
To find the percentage by which A is more than D:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{D} \right) \times 100 = \left( \frac{71.6}{100} \right) \times 100 = 71.6\% \]

### Final Answer
A is 71.6% more than D.

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