# Q. 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?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Correct answer: c) Both 1 and 2

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

Let’s analyze the problem step by step.

Let:

o = cost of one orange

m = cost of one mango

a = cost of one apple

Given:

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.

This can be written as:

4o + 6m + 8a = 2(1o + 2m + 5a)

4o + 6m + 8a = 2o + 4m + 10a

Simplifying:

Subtract 2o + 4m + 10a from both sides:

2o + 2m – 2a = 0

Divide by 2:

o + m = a**This confirms Statement 2: The total cost of one orange and one mango is equal to the cost of one apple.**

Now, let’s evaluate Statement 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.”

Expressed mathematically:

3o + 5m + 9a = 4o + 6m + 8a

Rearrange:

3o + 5m + 9a – 4o – 6m – 8a = 0

-o – m + a = 0

o + m = a

**This is the same as what we derived earlier, hence Statement 1 is also correct.**

Conclusion: Both statements 1 and 2 are correct.