The Confusing Question

One day, Kushal and Mehul went for a day out. It was a long day, and they both were tired. None of them wanted to drive the car. Mehul challenges Kushal to solve a riddle. If Kushal could give the correct answer, Mehul offers to drive the car, if not, Kushal will have to drive the car.

Mehul then asks Kushal "Agents Yellow, Red and Green each have a green badge, a yellow badge and a red badge, but none of them has a badge color that matches their name.

They met when called to a conference at headquarters. The Agent with the Green badge said, "I have a license to kill! to which Agent Red replied sarcastically: What, time? What color is each Agent's badge?" Can you tell me the answer?

Note that it`s the agent with the Green badge and not Agent Green talking to Agent Red. As the agent with the green badge has spoken to Agent Red, we know that Agent Red doesn`t have a green badge. We already know he doesn`t have a red badge. Therefore he has a yellow badge. The agent with the green badge cannot be Agent Red, nor can he be Agent Green, therefore he is Agent Yellow. So Agent Yellow has a Green badge, and Agent Red has a yellow badge, meaning Agent Green must have a red badge. Note that it`s the agent with the Green badge and not Agent Green talking to Agent Red. As the agent with the green badge has spoken to Agent Red, we know that Agent Red doesn`t have a green badge. We already know he doesn`t have a red badge. Therefore he has a yellow badge. The agent with the green badge cannot be Agent Red, nor can he be Agent Green, therefore he is Agent Yellow. So Agent Yellow has a Green badge, and Agent Red has a yellow badge, meaning Agent Green must have a red badge.