In the first four papers each of `100` marks, Rishi got `95,` `72 ,` `73,` `83` marks. If he wants an average of greater than or equal to `75` marks and less than `80` marks, find the range of marks he should score in the fifth paper.

Options

A. `52lexlt77`
B. `25ltxlt75`
C. `75ltxlt80`
D. `73ltxlt100`

Explanation

To find the range of marks Rishi should score in the fifth paper to achieve an average of greater than or equal to 75 and less than 80, we can follow these steps:

### Step 1: Calculate the total marks from the first four papers.
Rishi scored:
- Paper 1: 95
- Paper 2: 72
- Paper 3: 73
- Paper 4: 83

Total marks from the first four papers:
\[ 95 + 72 + 73 + 83 = 323 \]

### Step 2: Set up the average condition.
Let \( x \) be the marks Rishi scores in the fifth paper. The average of the five papers can be expressed as:
\[ \text{Average} = \frac{323 + x}{5} \]
We want this average to satisfy the condition:
\[ 75 \leq \frac{323 + x}{5} < 80 \]

### Step 3: Multiply the entire inequality by 5 to eliminate the fraction.
\[ 75 \times 5 \leq 323 + x < 80 \times 5 \]
This simplifies to:
\[ 375 \leq 323 + x < 400 \]

### Step 4: Solve for \( x \).
Subtract 323 from all parts of the inequality:
\[ 375 - 323 \leq x < 400 - 323 \]
Calculating the left and right sides:
\[ 52 \leq x < 77 \]

### Conclusion: Determine the range of marks for the fifth paper.
Thus, the range of marks Rishi should score in the fifth paper is:
\[ 52 \leq x < 77 \]