Divide 50 into two parts such that the sum of their reciprocals is 1/12. the…
2024
Divide 50 into two parts such that the sum of their reciprocals is 1/12. the numbers are
- A.
(20,30)
- B.
(28,22)
- C.
(27,23)
- D.
(24,26)
Attempted by 260 students.
Show answer & explanation
Correct answer: A
Solution:
Let the two numbers be x and 50 - x. We are given 1/x + 1/(50 - x) = 1/12.
Combine the fractions: 1/x + 1/(50 - x) = (50)/(x(50 - x)). So (50)/(x(50 - x)) = 1/12.
Cross-multiply: 50 · 12 = x(50 - x), so 600 = x(50 - x).
Expand and rearrange: 600 = 50x - x^2 ⇒ x^2 - 50x + 600 = 0.
Factor the quadratic: x^2 - 50x + 600 = (x - 20)(x - 30) = 0.
So x = 20 or x = 30. The two numbers are 20 and 30.
Check: 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12, which confirms the result.