The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes…
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 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Let costs be Q, M, A. Given $4Q + 6M + 8A = 2(Q + 2M + 5A)$, which simplifies to $2Q + 2M = 2A$, so $Q + M = A$. Statement 2 is directly $Q + M = A$ - correct. Statement 1: $3Q + 5M + 9A$ vs $4Q + 6M + 8A$; their difference is $A - Q - M = 0$, so they are equal - correct. Hence both statements are correct.