Question

Twenty times a positive integer is less than its square by 96. What is the integer
1. 24
2. 20
3. 30
4. 14

Answer 1

Correct Answer - Option 1 : 24

Let the positive integer be 'x'

Then, 20 times integer = 20x

Square of integer = x²

Twenty times a positive integer is less than its square by 96

x²  = 20x + 96

⇒ x² - 20x - 96 = 0

⇒ x² - 24x + 4x - 96 = 0

⇒ x ( x -24) + 4( x - 24) = 0

⇒ (x + 4) × (x -24) = 0

⇒ x = -4,  x = 24

∴ The positive integer is 24