A is 35% more than B, B is 25% less than C and C is 20% more than D. Which of the following is true?

Options

A. A)C is 1.5% less than A
B. B)D is 10% more than B
C. C)A is 1.25% more than C
D. D)D is 21.5% less than A

Answer

To solve the problem step by step, we need to express the relationships between A, B, C, and D mathematically.

### Step 1: Express A in terms of B
Given that A is 35% more than B, we can express this as:
\[ A = B + 0.35B = 1.35B \]

### Step 2: Express B in terms of C
We know that B is 25% less than C. Therefore, we can express B as:
\[ B = C - 0.25C = 0.75C \]

### Step 3: Express C in terms of D
It is given that C is 20% more than D. Thus, we can express C as:
\[ C = D + 0.20D = 1.20D \]

### Step 4: Substitute to find relationships
Now we will substitute the expressions we found in steps 2 and 3 back into the expression for A.

1. Substitute B in the equation for A:
\[ A = 1.35B = 1.35(0.75C) \]
\[ A = 1.0125C \]

2. Substitute C in the equation for A:
\[ C = 1.20D \]
\[ A = 1.0125(1.20D) \]
\[ A = 1.215D \]

### Step 5: Now, we can find the ratios
Now we can express A, B, C, and D in terms of D:
- \( D = D \)
- \( C = 1.20D \)
- \( B = 0.75C = 0.75(1.20D) = 0.90D \)
- \( A = 1.35B = 1.35(0.90D) = 1.215D \)

### Step 6: Analyze the relationships
Now we have:
- \( A = 1.215D \)
- \( B = 0.90D \)
- \( C = 1.20D \)

### Step 7: Compare A and C
To find out how much more A is than C:
\[ A = 1.215D \]
\[ C = 1.20D \]

Now, we can find the difference:
\[ A - C = 1.215D - 1.20D = 0.015D \]

To find the percentage difference:
\[ \text{Percentage} = \left( \frac{A - C}{C} \right) \times 100 = \left( \frac{0.015D}{1.20D} \right) \times 100 = \frac{0.015}{1.20} \times 100 = 1.25\% \]

### Conclusion
Thus, we can conclude that A is 1.25% more than C.