Final answer:
To find the marks obtained in the 7th paper, calculate the total marks for the first and last 7 papers, then subtract the total marks for all 13 papers and divide by 2, since the 7th paper is included in both subsets. The 7th paper's marks are 19.5.
Step-by-step explanation:
Finding the Marks Obtained in the 7th Paper
The question involves calculating the mark obtained in the 7th paper given the average of 13 papers and the average of subsets of these papers. To solve this, we will use the concept of the average (mean) to set up equations and solve for the unknown mark.
First, we find the total marks for all 13 papers by multiplying the average (40) by the number of papers (13):
Total marks for all 13 papers = Average × Number of papers
= 40 × 13
= 520 marks.
Next, we calculate the total marks for the first 7 papers:
Total marks for the first 7 papers = Average of the first 7 papers × Number of papers
= 42 × 7
= 294 marks.
We also calculate the total marks for the last 7 papers:
Total marks for the last 7 papers = Average of the last 7 papers × Number of papers
= 35 × 7
= 245 marks.
Notice that the 7th paper is counted in both the first and last sets of papers. To find the marks for the 7th paper, we'll add the total marks for the first 7 papers and the last 7 papers and then subtract the total marks for all 13 papers, leaving us with twice the marks of the 7th paper (since it's double-counted).
Marks obtained in the 7th paper = (Total marks for the first 7 papers + Total marks for the last 7 papers - Total marks for all 13 papers) / 2
= (294 + 245 - 520) / 2
= 19.5 marks.