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?

The correct option is Both 1 and 2.

Let us denote the cost of one orange, one mango, and one apple as $o$, $m$, and $a$ respectively.

From the given problem, we can write the first relationship as an equation:
$4o+6m+8a=2(o+2m+5a)$
Let us simplify this equation by expanding the right side:
$4o+6m+8a=2o+4m+10a$
Now, let us group the terms by bringing similar variables to the same side:
$4o-2o+6m-4m=10a-8a$
This simplifies to:
$2o+2m=2a$
Dividing both sides by 2, we get:
$o+m=a$

Now, let us analyze the two statements based on this relation:

Analysis of Statement 2:
Statement 2 states that "The total cost of one orange and one mango is equal to the cost of one apple."
This translates to the equation $o+m=a$, which is exactly the relationship we derived. Therefore, Statement 2 is correct.

Analysis of Statement 1:
Statement 1 states that "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."
Let us write down both sides of this statement and check if they are equal under our condition $a=o+m$:
First, the cost of 3 oranges, 5 mangoes, and 9 apples:
$\text{Cost 1}=3o+5m+9a$
Substitute $a=o+m$ into Cost 1:
$\text{Cost 1}=3o+5m+9(o+m)=3o+5m+9o+9m=12o+14m$
Next, the cost of 4 oranges, 6 mangoes, and 8 apples:
$\text{Cost 2}=4o+6m+8a$
Substitute $a=o+m$ into Cost 2:
$\text{Cost 2}=4o+6m+8(o+m)=4o+6m+8o+8m=12o+14m$
Since both costs simplify to the same expression ($12o+14m$), the two costs are indeed equal. Therefore, Statement 1 is correct.

Thus, both statements 1 and 2 are correct.