A is `20%` more than B, B is `25%` more than C, C is `50%` less than D and D is `10%` more than E. Which of the following is true?

Options

A. A is `17.5%` less than E
B. D is `30%` less than B
C. A is `40%` less than D
D. C is `24%` less than A

Answer

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

### Step 1: Define the variables
Let:
- C = x (we will express all other variables in terms of x)

### Step 2: Express B in terms of C
B is 25% more than C:
\[ B = C + 0.25C = 1.25C = 1.25x \]

### Step 3: Express A in terms of B
A is 20% more than B:
\[ A = B + 0.20B = 1.20B = 1.20(1.25x) = 1.50x \]

### Step 4: Express D in terms of C
C is 50% less than D:
\[ C = D - 0.50D = 0.50D \]
Thus,
\[ D = \frac{C}{0.50} = 2C = 2x \]

### Step 5: Express E in terms of D
D is 10% more than E:
\[ D = E + 0.10E = 1.10E \]
Thus,
\[ E = \frac{D}{1.10} = \frac{2x}{1.10} = \frac{20x}{11} \]

### Step 6: Combine the relationships
Now we have:
- A = 1.50x
- B = 1.25x
- C = x
- D = 2x
- E = \(\frac{20x}{11}\)

### Step 7: Find the ratio A to E
To find the ratio of A to E:
\[ A : E = 1.50x : \frac{20x}{11} \]
This simplifies to:
\[ A : E = 1.50 : \frac{20}{11} \]
To simplify further, multiply both sides by 11:
\[ A : E = 1.50 \times 11 : 20 = 16.5 : 20 \]
Now, we can convert this to a simpler ratio:
\[ A : E = 33 : 40 \]

### Step 8: Calculate the percentage difference
To find how much A is less than E:
\[ \text{Difference} = E - A = \frac{20x}{11} - 1.50x \]
Convert 1.50x to a fraction with a denominator of 11:
\[ 1.50x = \frac{16.5x}{11} \]
Now, substituting back:
\[ \text{Difference} = \frac{20x}{11} - \frac{16.5x}{11} = \frac{3.5x}{11} \]

Now, to find the percentage difference:
\[ \text{Percentage} = \left(\frac{\text{Difference}}{E}\right) \times 100 = \left(\frac{\frac{3.5x}{11}}{\frac{20x}{11}}\right) \times 100 = \left(\frac{3.5}{20}\right) \times 100 = 17.5\% \]

### Conclusion
Thus, A is 17.5% less than E.