# 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 Paper

**Explanation:**

## 4 oranges, 6 mangoes and 8 apples

Let’s approach this step-by-step:

1) Let’s define variables:

o = cost of one orange

m = cost of one mango

a = cost of one apple

2) From the given information:

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

3) Let’s simplify the right side:

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

4) Subtracting the right side from both sides:

2o + 2m – 2a = 0

o + m = a

5) Now, let’s examine the statements:

Statement 1: 3o + 5m + 9a = 4o + 6m + 8a

Subtracting the right side from both sides:

-o – m + a = 0

a = o + m

This is exactly what we derived in step 4, so Statement 1 is correct.

Statement 2: o + m = a

This is also exactly what we derived in step 4, so Statement 2 is also correct.