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 ✓ UPSC's answer
- (d) Neither 1 nor 2
Why the answer is (c)
• Let one orange, mango and apple cost O, M and A.
• The condition 4O + 6M + 8A = 2(O + 2M + 5A) = 2O + 4M + 10A simplifies to 2O + 2M = 2A, i.e. O + M = A. So Statement 2 is correct.
• Statement 1: (3O + 5M + 9A) − (4O + 6M + 8A) = A − O − M = 0, so the two totals are equal. Statement 1 is correct.
• Both statements are correct — option (c).
Why the other options are wrong
- (a) 1 only
- Statement 2 is also correct: the condition reduces to O + M = A.
- (b) 2 only
- Statement 1 is also correct: the two totals differ by A − O − M, which is 0.
- (d) Neither 1 nor 2
- Both statements follow from O + M = A, so 'neither' is wrong.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.