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

Answer 1

The Correct Option is B

Step 1: Define the variables

Let Ankita’s age be \( a \) and Nikita’s age be \( n \). 

Step 2: Use the given conditions

• \( a \times n = 240 \)
• \( 2n = a + 4 \)

Step 3: Express \( a \) in terms of \( n \)

\[ a = 2n - 4 \]

Step 4: Substitute this into the first equation

\[ (2n - 4) \times n = 240 \]

Step 5: Expand and simplify

\[ 2n^2 - 4n = 240 \] \[ 2n^2 - 4n - 240 = 0 \]

Step 6: Divide by 2

\[ n^2 - 2n - 120 = 0 \]

Step 7: Solve the quadratic equation

Using the quadratic formula: \[ n = \frac{2 \pm \sqrt{2^2 - 4(1)(-120)}}{2(1)} \] \[ = \frac{2 \pm \sqrt{4 + 480}}{2} \] \[ = \frac{2 \pm \sqrt{484}}{2} \]

Step 8: Find the possible values of \( n \)

\[ n = \frac{2 + 22}{2} = \frac{24}{2} = 12 \] \[ n = \frac{2 - 22}{2} = \frac{-20}{2} = -10 \]

Since age cannot be negative, we take \( n = 12 \).

Thus, Nikita’s age is 12.