The sum of two numbers is 45. The sum of their quotient and its reciprocal is…
2024
The sum of two numbers is 45. The sum of their quotient and its reciprocal is 2.5 (i.e. if the quotient of the two numbers is a/b, then a/b + b/a = 2.5). Find the product of the numbers.
Answer: C. 450 — Solution: Let the two numbers be a and b. Given a + b = 45 a/b + b/a = 2.5, which implies (a^2 + b^2)/ab = 2.5 Compute (a + b)^2: (a + b)^2 = a^2 + b^2 + 2ab…
- A.
600
- B.
780
- C.
450
- D.
500
Attempted by 272 students.
Show answer & explanation
Correct answer: C
Solution:
Let the two numbers be a and b. Given
a + b = 45
a/b + b/a = 2.5, which implies (a^2 + b^2)/ab = 2.5
Compute (a + b)^2:
(a + b)^2 = a^2 + b^2 + 2ab = 45^2 = 2025, so a^2 + b^2 = 2025 - 2ab.
Substitute into (a^2 + b^2)/ab = 2.5 to get (2025 - 2ab)/ab = 2.5.
So 2025/ab - 2 = 2.5, hence 2025/ab = 4.5 and 4.5·ab = 2025.
Therefore ab = 2025/4.5 = 450.
Answer: 450