The average marks scored by Ajay in certain number of test is 84. He scored 100 marks in his last test. His average score of all these tests is 86, then the total number of tests he appeared is.

Options

A. 8
B. 7
C. 9
D. 10

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the variables
Let \( n \) be the total number of tests Ajay appeared for before his last test. According to the problem, his average score for these tests is 84.

### Step 2: Calculate the total marks before the last test
The total marks scored by Ajay in these \( n \) tests can be calculated as:
\[ \text{Total marks} = \text{Average} \times \text{Number of tests} = 84n \]

### Step 3: Include the last test score
Ajay scored 100 marks in his last test. Therefore, the total marks after including the last test becomes:
\[ \text{Total marks after last test} = 84n + 100 \]

### Step 4: Set up the equation for the new average
After including the last test, the total number of tests becomes \( n + 1 \). The new average score is given as 86. We can set up the equation:
\[ \frac{84n + 100}{n + 1} = 86 \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 84n + 100 = 86(n + 1) \]

### Step 6: Expand and simplify the equation
Expanding the right side:
\[ 84n + 100 = 86n + 86 \]
Now, rearranging the equation to isolate \( n \):
\[ 100 - 86 = 86n - 84n \]
\[ 14 = 2n \]

### Step 7: Solve for \( n \)
Dividing both sides by 2:
\[ n = 7 \]

### Step 8: Calculate the total number of tests
Since \( n \) is the number of tests before the last one, the total number of tests Ajay appeared for is:
\[ \text{Total tests} = n + 1 = 7 + 1 = 8 \]

### Final Answer
Ajay appeared for a total of **8 tests**.

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