The sum of two positive numbers is 100. After subtracting 5 from each number, the product of the resulting numbers is 0. One of the original numbers is: A. 10 B. 85 C. 90 D. 95

GATE 2020 · General Aptitude · Number System · medium

Answer: One of the original numbers is 95 (Option D)

1. Set up the variables: Let the two positive numbers be x and y. Then y = 100 - x.
2. Apply the product condition: Substitute y = 100 - x: (x - 5)(100 - x - 5) = (x - 5)(95 - x) = 0.
3. Solve for x: Case 1: x - 5 = 0 => x = 5 (so y = 95). Case 2: 95 - x = 0 => x = 95 (so y = 5). Both cases give the pair {5, 95}.
4. Identify the answer from options: The options are 10, 85, 90, 95. Only D = 95 appears in the solution set {5, 95}. Answer is D.