The average marks of a student in 10 papers are 80. If the heighest and the lowest score are not considered the average is 81. If his heighest score is 92. Find the lowest score.

Options

A. 55
B. 60
C. 62
D. Can not be determined

Answer

To solve the problem step by step, we will follow the given information and apply the necessary calculations.

### Step 1: Calculate the total marks for 10 papers
The average marks of a student in 10 papers are given as 80. To find the total marks, we can use the formula:

\[ \text{Total Marks} = \text{Average} \times \text{Number of Papers} \]

Substituting the values:

\[ \text{Total Marks} = 80 \times 10 = 800 \]

### Step 2: Calculate the total marks for 8 papers (excluding highest and lowest scores)
When the highest and lowest scores are not considered, the average becomes 81 for the remaining 8 papers. We can calculate the total marks for these 8 papers using the same formula:

\[ \text{Total Marks for 8 Papers} = \text{Average} \times \text{Number of Papers} \]

Substituting the values:

\[ \text{Total Marks for 8 Papers} = 81 \times 8 = 648 \]

### Step 3: Find the sum of the highest and lowest scores
Now, we need to find the sum of the highest and lowest scores. We know the total marks for all 10 papers and the total marks for the 8 papers. Thus, we can find the sum of the highest and lowest scores by subtracting the total marks for 8 papers from the total marks for 10 papers:

\[ \text{Sum of Highest and Lowest Scores} = \text{Total Marks} - \text{Total Marks for 8 Papers} \]

Substituting the values:

\[ \text{Sum of Highest and Lowest Scores} = 800 - 648 = 152 \]

### Step 4: Use the highest score to find the lowest score
We are given that the highest score is 92. Let the lowest score be \( L \). We can set up the equation:

\[ \text{Highest Score} + \text{Lowest Score} = 152 \]
\[ 92 + L = 152 \]

Now, we can solve for \( L \):

\[ L = 152 - 92 = 60 \]

### Conclusion
The lowest score is 60.

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