The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples.

Let O, M, and A represent the costs of one orange, one mango, and one apple, respectively.

According to the problem statement, 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 can be expressed algebraically as:

4O + 6M + 8A = 2(1O + 2M + 5A)

Simplifying the equation:

4O + 6M + 8A = 2O + 4M + 10A

Rearranging the terms to one side:

4O - 2O + 6M - 4M = 10A - 8A

2O + 2M = 2A

Dividing the entire equation by 2, the fundamental relationship between the costs is established:

O + M = A

Correct Option (C)

Both1and2

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.

This statement can be written as an equation:

3O + 5M + 9A = 4O + 6M + 8A

To verify this statement, rearrange the terms:

9A - 8A = 4O - 3O + 6M - 5M

A = O + M

This derived equality (A = O + M) precisely matches the fundamental relationship established from the problem's initial condition. Therefore, Statement 1 is correct.

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

This statement directly translates to the algebraic expression:

O + M = A

This is exactly the fundamental relationship derived from the problem's initial condition. Therefore, Statement 2 is correct.

Since both Statement 1 and Statement 2 are correct, option C is the correct answer.

Incorrect Options

Options A, B, and D are incorrect because both statements are valid and consistent with the information provided in the problem and the derived cost relationship (O + M = A).