In an examination in which maximum marks were 800, A gets 15% more than B, B gets 25% more than C and C gets 10% less than D. If A got 598 marks, then what percentage of full marks did D get (approximately)?

Options

A. `45.8 %`
B. `62.3 %`
C. `57.8 %`
D. None of these

Answer

To solve the problem step by step, we will first establish the relationships between the marks obtained by A, B, C, and D based on the information provided.

### Step 1: Establish the relationship between A and B
Given that A gets 15% more than B, we can express this relationship mathematically:
\[ A = B + 0.15B = 1.15B \]
This can also be rewritten as:
\[ A = \frac{115}{100}B \]
or
\[ B = \frac{100}{115}A \]

### Step 2: Substitute the value of A
We know A got 598 marks. So we can substitute this value into the equation:
\[ B = \frac{100}{115} \times 598 \]

### Step 3: Calculate B
Now we will calculate B:
\[ B = \frac{100 \times 598}{115} \]
\[ B = \frac{59800}{115} \]
\[ B \approx 520 \]

### Step 4: Establish the relationship between B and C
Next, we know that B gets 25% more than C:
\[ B = C + 0.25C = 1.25C \]
This can be rewritten as:
\[ C = \frac{B}{1.25} = \frac{4}{5}B \]

### Step 5: Substitute the value of B
Now we substitute the value of B we found:
\[ C = \frac{4}{5} \times 520 \]

### Step 6: Calculate C
Calculating C gives us:
\[ C = \frac{4 \times 520}{5} \]
\[ C = \frac{2080}{5} \]
\[ C \approx 416 \]

### Step 7: Establish the relationship between C and D
We know that C gets 10% less than D:
\[ C = D - 0.10D = 0.90D \]
This can be rewritten as:
\[ D = \frac{C}{0.90} \]

### Step 8: Substitute the value of C
Now we substitute the value of C:
\[ D = \frac{416}{0.90} \]

### Step 9: Calculate D
Calculating D gives us:
\[ D = \frac{416}{0.90} \]
\[ D \approx 462.22 \]

### Step 10: Calculate the percentage of full marks D got
Finally, we need to find out what percentage of the maximum marks (800) D got:
\[ \text{Percentage of full marks} = \left( \frac{D}{800} \right) \times 100 \]
\[ \text{Percentage of full marks} = \left( \frac{462.22}{800} \right) \times 100 \]
\[ \text{Percentage of full marks} \approx 57.78\% \]

### Final Answer
Thus, D got approximately **57.78%** of the full marks.