Let's assume the cost of one orange is O, one mango is M, and one apple is A.

Given:

• The total cost of 4 oranges, 6 mangoes, and 8 apples is twice the total cost of 1 orange, 2 mangoes, and 5 apples. This translates to the equation:
  • $4O + 6M + 8A = 2 \times (O + 2M + 5A)$

Now, let's simplify this equation:

• $4O + 6M + 8A = 2(O + 2M + 5A)$
• $4O + 6M + 8A = 2O + 4M + 10A$
• $4O + 6M + 8A - 2O - 4M - 10A = 0$
• $2O + 2M - 2A = 0$
• $O + M = A$
  • This means the cost of 1 orange and 1 mango is equal to the cost of 1 apple.

Now, let's evaluate the statements:

• Statement 1: The total cost of 3 oranges, 5 mangoes, and 9 apples is equal to the total cost of 4 oranges, 6 mangoes, and 8 apples.

  • $3O + 5M + 9A = 4O + 6M + 8A$
  • Using the relation $O + M = A$, substitute A in both sides:
    • $3O + 5M + 9(O + M) = 4O + 6M + 8(O + M)$
    • Simplifying both sides gives us the same expression, so Statement 1 is correct.

• Statement 2: The total cost of 1 orange and 1 mango is equal to the cost of 1 apple.

  • From the equation we derived earlier, Statement 2 is correct.

Conclusion: Both statements are correct.

Answer: C. Both 1 and 2