The total cost of 4 oranges 6 mangoes and 8 apples is equal to twice the total cost of 1 orange 2 ma...........

Math and Mental Ability Profit and loss

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 ?

This questions was previously asked in

UPSC CSAT, Previous year (2024)

View All CSAT Previous Year Papers

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

To solve the problem, let's use algebra:

- Let the cost of an orange be O, a mango be M, and an apple be A.

- According to the problem, the cost of 4O + 6M + 8A equals twice the cost of O + 2M + 5A.

- This translates to: 4O + 6M + 8A = 2(O + 2M + 5A), simplifying gives 4O + 6M + 8A = 2O + 4M + 10A.

- Rearrange it to get: 2O + 2M = 2A, which simplifies to O + M = A.

Now, examine the statements:

1. The total cost of 3 oranges, 5 mangoes, and 9 apples equals the total cost of 4 oranges, 6 mangoes, and 8 apples. This is true because, substituting O + M = A in both expressions gives identical costs.

2. The total cost of one orange and one mango is equal to the cost of one apple. Given the simplification, O + M = A, this is correct.

- Option:3 is correct; both statements are true.