A student got 85,87,91,82, 90 and x marks in all his subjects. His average marks were found to be 85. What should come in place of x ?

Options

A. 83
B. 75
C. 77
D. 73

Answer

To find the value of x in the given problem, we will follow these steps:

### Step 1: Understand the average formula
The average (A) of a set of numbers is calculated using the formula:
\[ A = \frac{\text{Total Marks}}{\text{Number of Subjects}} \]

### Step 2: Identify the given values
In this case, the average marks are given as 85, and the marks obtained by the student in five subjects are 85, 87, 91, 82, and 90. We also have the unknown marks x.

### Step 3: Count the total number of subjects
The total number of subjects is 6 (5 known marks + 1 unknown mark x).

### Step 4: Set up the equation using the average formula
Using the average formula, we can set up the equation:
\[ 85 = \frac{85 + 87 + 91 + 82 + 90 + x}{6} \]

### Step 5: Calculate the total marks without x
First, we calculate the sum of the known marks:
\[ 85 + 87 + 91 + 82 + 90 = 435 \]

### Step 6: Substitute the total marks into the equation
Now, substitute the total marks into the equation:
\[ 85 = \frac{435 + x}{6} \]

### Step 7: Multiply both sides by 6 to eliminate the fraction
To eliminate the fraction, multiply both sides by 6:
\[ 85 \times 6 = 435 + x \]
\[ 510 = 435 + x \]

### Step 8: Solve for x
Now, isolate x by subtracting 435 from both sides:
\[ x = 510 - 435 \]
\[ x = 75 \]

### Conclusion
The value of x should be 75.

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