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?

1. A. 1 only
2. B. 2 only
3. C. Both 1 and 2
4. D. Neither 1 nor 2

Answer: C

Explanation

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.