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.