In an examination, A got 10% marks less than B. B got 25% marks more than C. C got 20% marks less than D. If A got 360 marks out of 500, the percentage of marks obtained by D was

Options

A. 70
B. 75
C. 80
D. 85

Answer

To solve the problem step by step, we need to establish the relationships between the marks obtained by A, B, C, and D based on the information given.

### Step 1: Determine B's marks from A's marks
We know that A got 10% marks less than B. If A got 360 marks, we can express this relationship mathematically.

Let B's marks be represented as \( B \).

According to the problem:
\[ A = B - 0.10B \]
\[ A = 0.90B \]

Substituting A's marks:
\[ 360 = 0.90B \]

Now, we can solve for B:
\[ B = \frac{360}{0.90} \]
\[ B = 400 \]

### Step 2: Determine C's marks from B's marks
Next, we know that B got 25% marks more than C. We can express this relationship as well.

Let C's marks be represented as \( C \).

According to the problem:
\[ B = C + 0.25C \]
\[ B = 1.25C \]

Substituting B's marks:
\[ 400 = 1.25C \]

Now, we can solve for C:
\[ C = \frac{400}{1.25} \]
\[ C = 320 \]

### Step 3: Determine D's marks from C's marks
Now we know that C got 20% marks less than D. We can express this relationship as follows.

Let D's marks be represented as \( D \).

According to the problem:
\[ C = D - 0.20D \]
\[ C = 0.80D \]

Substituting C's marks:
\[ 320 = 0.80D \]

Now, we can solve for D:
\[ D = \frac{320}{0.80} \]
\[ D = 400 \]

### Step 4: Calculate the percentage of marks obtained by D
Now that we have D's marks, we can calculate the percentage of marks obtained by D. The total marks are 500.

Percentage of marks obtained by D:
\[ \text{Percentage} = \left( \frac{D}{\text{Total Marks}} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{400}{500} \right) \times 100 \]
\[ \text{Percentage} = 80\% \]

### Final Answer
The percentage of marks obtained by D is **80%**.

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