The average of 13 results is 60 . If the average of first 7 Results is 59 and that of last 7 results is 61 , what will be the seventh results ?

Options

A. 90
B. 50
C. 75
D. 60

Answer

To solve the problem step by step, we will use the information provided about the averages of the results.

### Step 1: Calculate the sum of the 13 results.
The average of the 13 results is given as 60. To find the sum of these results, we can use the formula for average:

\[ \text{Sum} = \text{Average} \times \text{Number of Results} \]

So, the sum of the 13 results is:

\[ \text{Sum of 13 results} = 60 \times 13 = 780 \]

### Step 2: Calculate the sum of the first 7 results.
The average of the first 7 results is given as 59. Using the same formula:

\[ \text{Sum of first 7 results} = 59 \times 7 = 413 \]

### Step 3: Calculate the sum of the last 7 results.
The average of the last 7 results is given as 61. Again, using the formula:

\[ \text{Sum of last 7 results} = 61 \times 7 = 427 \]

### Step 4: Find the total of the first 7 and last 7 results.
Now, we need to find the total of the first 7 results and the last 7 results:

\[ \text{Total of first 7 and last 7 results} = 413 + 427 = 840 \]

### Step 5: Calculate the 7th result.
Since the 7th result is included in both the first 7 results and the last 7 results, we need to subtract the sum of the first 7 and last 7 results from the sum of the 13 results to find the 7th result:

\[ \text{7th result} = \text{Sum of 13 results} - (\text{Sum of first 7 results} + \text{Sum of last 7 results}) + \text{7th result} \]

This can be simplified to:

\[ \text{7th result} = 780 - 840 + \text{7th result} \]

To isolate the 7th result, we can rearrange this:

\[ \text{7th result} = 780 - 840 + \text{7th result} \]

Since we have counted the 7th result twice in the total of 840, we can express it as:

\[ \text{7th result} = 780 - 840 + \text{7th result} \]

This simplifies to:

\[ \text{7th result} = 60 \]

### Final Answer:
The 7th result is **60**.

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