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?

Question

Accepted Answer

The correct answer is option C. Let O, M, and A represent the costs of one orange, one mango, and one apple, respectively.

From the given information:
4O + 6M + 8A = 2(1O + 2M + 5A)
4O + 6M + 8A = 2O + 4M + 10A
Rearranging the terms to one side:
(4O - 2O) + (6M - 4M) + (8A - 10A) = 0
2O + 2M - 2A = 0
Dividing by 2:
O + M - A = 0
O + M = A
This equation directly matches Statement 2. So, Statement 2 is correct.

Now, let's check Statement 1:
Is 3O + 5M + 9A = 4O + 6M + 8A?
Rearranging the terms:
9A - 8A = (4O - 3O) + (6M - 5M)
A = O + M
This equation is identical to the relationship we derived from the initial problem statement. Therefore, Statement 1 is also correct.

Since both Statement 1 and Statement 2 are correct, the answer is (C). This question tests algebraic manipulation and problem-solving skills.

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