In a series of tests, A appeared for 8 tests Each test was marked out of 30 and averages 25. However, while checking his files, A could only find 7 of the 8 tests. For these he scored 29 26, 18 ,20, 27, 24 and 29. Determine how many marks he scored for the eighth test.

Answer

To determine how many marks A scored in the eighth test, we can follow these steps:

### Step 1: Understand the given information
A appeared for 8 tests, and the average score across these tests is 25. The scores for 7 of the tests are given as: 29, 26, 18, 20, 27, 24, and 29.

### Step 2: Calculate the total score for 8 tests
Since the average score is given as 25, we can calculate the total score for all 8 tests using the formula for average:

\[ \text{Average} = \frac{\text{Total Score}}{\text{Number of Tests}} \]

Rearranging this gives us:

\[ \text{Total Score} = \text{Average} \times \text{Number of Tests} \]

Substituting the values:

\[ \text{Total Score} = 25 \times 8 = 200 \]

### Step 3: Calculate the sum of the known scores
Now, we need to sum the scores of the 7 tests that A has:

\[ 29 + 26 + 18 + 20 + 27 + 24 + 29 \]

Calculating this step-by-step:

- \(29 + 26 = 55\)
- \(55 + 18 = 73\)
- \(73 + 20 = 93\)
- \(93 + 27 = 120\)
- \(120 + 24 = 144\)
- \(144 + 29 = 173\)

So, the total score for the 7 tests is 173.

### Step 4: Determine the score for the eighth test
Let \(X\) be the score for the eighth test. We know that the total score for all 8 tests is 200, so we can set up the equation:

\[ 173 + X = 200 \]

### Step 5: Solve for \(X\)
Now, we can solve for \(X\):

\[ X = 200 - 173 = 27 \]

### Conclusion
A scored **27 marks** in the eighth test.

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