The product of the ages of Ankit and Nikita is 240. If twice the age of Nikita is more than Ankit's age by 4 years, What is Nikita's age?

Question: The product of the ages of Ankit and Nikita is 240. If twice the age of Nikita is more than Ankit's age by 4 years, What is Nikita's age?

Solution:
Given that,
Product of the ages of Ankit and Nikita = 240
And two times age of Nikita is more than Ankit's age by 4 years

Now,
Let Ankit's age be x years, then, Nikita's age = 240/x years
Two times age of Nikita is more than Ankit's age by 4 years

ATQ,
2 × (240/x) - x = 4
⇒ 480 - x2 = 4x
⇒ x² + 4x - 480 = 0
⇒ x² + 24x - 20x - 480 = 0
⇒ x(x + 24) - 20(x + 24) = 0
⇒ (x + 24)(x - 20) = 0
∴ x + 24 = 0
⇒ x = - 24 [Neglecting the negative value]
Or, x - 20 = 0
∴ x = 20

∴ Nikita's age = 240/20 = 12 Years

So, the Nikita's age is 12 years