Shortcut Trick
Check the options to satisfy the condition: Number + 20/Number = 9
Option (4): 5 + 20/5 ⇒ 5 + 4 = 9.
Condition satisfied.
∴ The correct answer is 5.
Alternate Method
Given: Sum of a non-zero number and 20 times its reciprocal is 9.
Formula Used: Let the number be x. Equation: x + 20(1/x) = 9
⇒ x + 20/x = 9
⇒ (x2 + 20) / x = 9
⇒ x2 + 20 = 9x
⇒ x2 − 9x + 20 = 0
⇒ x2 − 5x − 4x + 20 = 0
⇒ x(x − 5) − 4(x − 5) = 0
⇒ (x − 5)(x − 4) = 0
⇒ x = 5 or x = 4
From the given options, 5 is the correct choice.
∴ The correct answer is 5.
Additional Information
Quadratic Equation Roots
For ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.
Reciprocal Relationship
If a number is x, its multiplicative inverse or reciprocal is 1/x, where x ≠ 0.
Nature of Roots
Discriminant D = b2 − 4ac helps determine if roots are real, equal, or imaginary.