Let's break down the problem step by step.

We are given the following information:

• First Exam:

  • Ravi scored 8 more marks than Priya.
  • Let Priya's score be $p_1$, so Ravi's score is $p_1 + 8$.

• Second Exam:

  • Ravi scored 6 more marks than Priya.
  • Let Priya's score be $p_2$, so Ravi's score is $p_2 + 6$.

• Third Exam:

  • Let Priya's score be $p_3$, and Ravi's score be $r_3$.

• We are also told that Priya's average score over the three exams is 5 marks higher than Ravi's average score.

Thus, the relationships we have are:

1. Ravi's total score: $(p_1 + 8) + (p_2 + 6) + r_3$
2. Priya's total score: $p_1 + p_2 + p_3$

Their respective averages:

$\text{Ravi's average} = \frac{(p_1 + 8) + (p_2 + 6) + r_3}{3}$ $\text{Priya's average} = \frac{p_1 + p_2 + p_3}{3}$

According to the problem, Priya's average score is 5 more than Ravi's average score:

$\frac{p_1 + p_2 + p_3}{3} = \frac{(p_1 + 8) + (p_2 + 6) + r_3}{3} + 5$

Multiplying both sides by 3 to eliminate the fractions:

$p_1 + p_2 + p_3 = (p_1 + 8) + (p_2 + 6) + r_3 + 15$

Simplifying the equation:

$p_1 + p_2 + p_3 = p_1 + p_2 + r_3 + 29$

Canceling $p_1$ and $p_2$ on both sides:

$p_3 = r_3 + 29$

Thus, Priya's score in the third exam is 29 marks more than Ravi's score in the third exam.

Let me know if you'd like any additional details or clarifications! Here are some related questions:

1. How would the result change if the difference in their average scores was different?
2. How can you verify the solution by substituting hypothetical values for $p_1$, $p_2$, and $p_3$?
3. What if the difference in scores was the same across all exams?
4. Can this type of problem be modeled using matrices for multiple students?
5. How would this problem change if one exam was weighted more than the others?

Tip: Always remember to clearly define your variables and set up equations carefully when solving word problems like this one.