In an examination, A secured `25% ` more marks than B. B secured `10% ` less marks than C. C secured `25% `more marks than D. If D secured 320 marks out of 500. How many marks did A secure?

Answer

To solve the problem step by step, let's define the marks secured by each student based on the information provided.

1. **Marks of D**:
- D secured 320 marks.
- Let's denote D's marks as \( D = 320 \).

2. **Marks of C**:
- C secured 25% more marks than D.
- To find C's marks, we calculate:
\[ C = D + 25\% \text{ of } D = D + 0.25D = 1.25D \]
- Substituting D's value:
\[ C = 1.25 \times 320 = 400 \]

3. **Marks of B**:
- B secured 10% less marks than C.
- To find B's marks, we calculate:
\[ B = C - 10\% \text{ of } C = C - 0.1C = 0.9C \]
- Substituting C's value:
\[ B = 0.9 \times 400 = 360 \]

4. **Marks of A**:
- A secured 25% more marks than B.
- To find A's marks, we calculate:
\[ A = B + 25\% \text{ of } B = B + 0.25B = 1.25B \]
- Substituting B's value:
\[ A = 1.25 \times 360 = 450 \]

Thus, A secured **450 marks**.