Question

At an IIM entrepreneurship summit, two young founders, Karan and Deepak, introduced their startup. In their quirky opening, they said "The product of our ages is 240. And just like in our startup strategy, twice Deepak's age is 4 years more than Karan's age. How old was Deepak two years ago?"

• A. 8 Years
• B. 15 Years
• C. 6 Years
• D. 10 Years

Hint:

When solving age-related problems, set up equations based on the given relationships and solve the system of equations.

Answer 1

The Correct Option is D

Let Karan's age be \( K \) and Deepak's age be \( D \). The two given conditions are: 

1. \( K \times D = 240 \) 

2. \( 2D = K + 4 \) 

From the second equation, solve for \( K \): \[ K = 2D - 4 \] Substitute this into the first equation: \[ (2D - 4) \times D = 240 \] Simplifying: \[ 2D^2 - 4D = 240 \] \[ 2D^2 - 4D - 240 = 0 \] Divide the equation by 2: \[ D^2 - 2D - 120 = 0 \] Now solve this quadratic equation using the quadratic formula: \[ D = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-120)}}{2(1)} \] \[ D = \frac{2 \pm \sqrt{4 + 480}}{2} \] \[ D = \frac{2 \pm \sqrt{484}}{2} \] \[ D = \frac{2 \pm 22}{2} \] Thus, \( D = \frac{2 + 22}{2} = 12 \) or \( D = \frac{2 - 22}{2} = -10 \). Since age cannot be negative, we take \( D = 12 \). 

Therefore, Deepak is currently 12 years old, and two years ago, he was \( 12 - 2 = 10 \) years old. Thus, the answer is \( 10 \) years.