Hint: In the question, we are asked about the nature of the charged object. For this we can use the concept that like charges repel each other whereas unlike charges attract each other. This means that a negative charge will attract a positive charge but it will repel a negative charge.
From Coulomb's law of electrostatics, we know that any two charged bodies in the universe will exert a force on each other, which is called electrostatic force. Now, electrostatic force can be attractive or repulsive in nature. The nature of the force depends on the charge on the bodies.
If the charges on both the bodies are of the same nature (not necessarily equal) then the two bodies will repel each other. This means that if either the bodies are positively charged or both the bodies are negatively charged, then they will repel each other.
If the charges on both the bodies are opposite nature (meaning one positively charged and other negatively charged) then the two bodies will attract each other. Therefore, if a negatively charged object repels another charged object on keeping close to that object, then this means that the other object has to be negatively charged.
Thus, option B negative, is correct.
Note: In the solution, we have mentioned that, “Like charges repel each other and unlike charges attract each other.” It happens because we know that the size of protons is much larger and heavier than electrons. So, two electrons of both objects will have a negative charge, so their lines of force get repelled. This way, two electrons will tend to repel each other because both will have a negative charge.