The average of marks of 15 papers is 45. The average of marks of the first 8 papers is 48 and that of the last 8 papers is 40. The marks of the eight paper will be:

29

The correct answer is Option (1) → 29

Let the marks of the 8th paper be x.

Step 1: Total marks of all 15 papers

$15 \times 45 = 675$

Step 2: Total marks of first 8 papers

$48 \times 48 = 38$

Step 3: Total marks of last 8 papers

$8 \times 40 = 320$

The 8th paper is included in both the first 8 and the last 8 papers, so it is counted twice.

$\text{First 8} + \text{Last 8} = \text{Total 15} + \text{Marks of 8th paper}$

$384 + 320 = 675 + x$

$704 = 675 + x$

$x = 29$