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

Which of the statements given above is/are correct?

Correct Option: (c) Both 1 and 2

Let the costs of an orange, a mango, and an apple be O, M, and A respectively. We are given that: 4O + 6M + 8A = 2 × (1O + 2M + 5A) ⇒ 4O + 6M + 8A = 2O + 4M + 10A. Subtracting 2O + 4M + 8A from both sides yields: 2O + 2M = 2A. Dividing by 2, we get: O + M = A. Thus, the cost of one orange and one mango is equal to the cost of one apple. This proves Statement 2 is correct. Now, let us evaluate Statement 1: Total cost of 3 oranges, 5 mangoes and 9 apples = 3O + 5M + 9A. Using A = O + M, this becomes: 3O + 5M + 9(O + M) = 12O + 14M. Total cost of 4 oranges, 6 mangoes and 8 apples = 4O + 6M + 8A. Using A = O + M, this becomes: 4O + 6M + 8(O + M) = 12O + 14M. Since both expressions are equal to 12O + 14M, Statement 1 is also correct. Since both statements are correct, option (c) is the correct answer.