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?
Answer & explanation
Answer: (c) Both 1 and 2
4O + 6M + 8A = 2(O + 2M + 5A) simplifies to O + M = A, which is statement 2. Statement 1 then follows, because 3O + 5M + 9A differs from 4O + 6M + 8A by A − O − M = 0.
- Let the prices be O, M and A. Then 4O + 6M + 8A = 2O + 4M + 10A.
- So 2O + 2M = 2A, i.e. O + M = A. Statement 2 is correct.
- (3O + 5M + 9A) − (4O + 6M + 8A) = A − O − M = 0. Statement 1 is correct.
- Check with O = 1, M = 2, A = 3: 4 + 12 + 24 = 40 = 2 × (1 + 4 + 15), and 3 + 10 + 27 = 40 as well.
- ✓ 1. The two totals differ by A − O − M, which is 0 because O + M = A.
- ✓ 2. Simplifying the given condition gives exactly O + M = A.
Remember · Simplify the given condition first; then test each statement by subtracting one side from the other.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·