Question

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

• A. \( 21 \)
• B. \( 12 \)
• C. \( 15 \)
• D. \( 20 \)
• E.

Hint:

For age-related problems, set up equations based on the given relations and solve the quadratic equation for the unknowns.

Answer 1

The Correct Option is B

Let Ankita's age be \( a \) and Nikita's age be \( n \). From the given conditions: \[ a \times n = 240 \quad \text{and} \quad 2n = a + 4 \] From the second equation, express \( a \) in terms of \( n \): \[ a = 2n - 4 \] Substitute this into the first equation: \[ (2n - 4) \times n = 240 \] Expanding and simplifying: \[ 2n^2 - 4n = 240 \quad \Rightarrow \quad 2n^2 - 4n - 240 = 0 \] Dividing by 2: \[ n^2 - 2n - 120 = 0 \] Solving this quadratic equation: \[ n = \frac{2 \pm \sqrt{2^2 - 4(1)(-120)}}{2(1)} = \frac{2 \pm \sqrt{4 + 480}}{2} = \frac{2 \pm \sqrt{484}}{2} \] \[ n = \frac{2 \pm 22}{2} \] Thus, \( n = 12 \) or \( n = 15 \). Therefore, Nikita's age is 12.