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 the costs of one orange, mango, and apple be $O$, $M$, and $A$ respectively.
• The given condition is $4O + 6M + 8A = 2(1O + 2M + 5A)$, which simplifies to $4O + 6M + 8A = 2O + 4M + 10A$.
• Rearranging terms yields $2O + 2M = 2A$, or $O + M = A$.
• Statement 2 directly states that the cost of one orange and one mango equals the cost of one apple ($O + M = A$), so Statement 2 is correct.
• To check Statement 1, substitute $A = O + M$ into the expression for 3 oranges, 5 mangoes, and 9 apples: $3O + 5M + 9(O + M) = 12O + 14M$.
• The cost of 4 oranges, 6 mangoes, and 8 apples is $4O + 6M + 8(O + M) = 12O + 14M$.
• Since both expressions equal $12O + 14M$, Statement 1 is also correct, making option (c) the right answer.
Why the other options are wrong
- (a) 1 only
- Statement 2 is also correct because the derived equation $O + M = A$ directly validates it.
- (b) 2 only
- Statement 1 is also correct because substituting $A = O + M$ shows both sides of the equation are equal.
- (d) Neither 1 nor 2
- Both statements are mathematically correct based on the derived relationship $O + M = A$.
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.