To summarize the above explanations:

In our example question, Bagheer makes the statement, “I am a liar”, which implies that Bagheer is the alternator. Also, Aman said that he is an alternator, which implies that he can be either a liar or an alternator. Now, since Bagheer is the alternator, Aman is definitely the liar. This leaves us with Chiru as the truth-teller. Since Bagheer is the alternator, so the statements proceeding/preceding the statement, “I am a liar” are true, we can conclude that Aman is not a Doctor. Also as Chiru is a truth-teller, according to his statements, Bagheer is not a painter and he himself is not a painter, thus Aman is the painter. Now, Bagheer’s first statement is a lie (since third statememt is also a lie, so the order for Bagheer’s statements will be 1st-false,2nd-true,3rd-false), this means Chiru is not an athlete, which leaves us with the only option for Chiru as Doctor and Bagheer will then be an athlete. To summarize our findings:

So the answer to the question, ‘Who is a Doctor’,is Chiru.

Other statements such as, “I am a truth-teller”, can be made by all the three categories of person and so will not be of much help to us.

STEP 2: In some cases, where none of the four statements as mentioned in step 1 was made by anyone, we will use the assumption-iteration method.In this method we will assume the first person as the truth-teller and based on his statements we will try to find conflicts or contradictions that may arise due to the statements made by others. We will also use the assumptions-iteration method when statement 3 or 4 mentioned in step 1 is made by anyone as these statements will leave us with two options.Consider the following example:

Utkarsh, Ravi and Shivam made the following statements regarding the type of vehicle they own. Each one of them belongs to exactly one category of truth-teller, liar or alternator. Only one among them is a truth-teller. Further, we know each of them own a different vehicle and each of them own exactly one among car, cycle and bike.

Now, Utkarsh says that he is not an alternator and as per step 1 we know that he can be a truth-teller or an alternator. To proceed with the approach, we will first assume that Utkarsh is the truth-teller and all the statements are true. We know exactly one among them is a truth –teller and we already assumed Utkarsh as the truth-teller.The question does not specifically mention the exact number of each category. From Utkarsh’s statements, we know neither Shivam owns a car nor Ravi. Reading Ravi’s statements, since his last statement is true so he should be an alternator (he can’t be the truth-teller as there is only one truth-teller which we already assumed as Utkarsh). This implies his second statement should be false but as per the statement made by Ravi, the second statement is also true. This is a contradiction to our assumption which means that our assumption is wrong.

We have to go for the second interation knowing Utkarsh is the alternator. As he is not the truth-teller, he has to be an alternator. His second statement is false which automatically makes his first and second statements true. We can deduce that Utkarsh owns a car as none of Ravi and Shivam owns a car as per Utkarsh’s statements. Shivam’s first statement is a lie so he can be a liar or an alternator. Since there is one truth-teller and the only option for the truth-teller is Ravi thus we can say Ravi is the truth-teller. This makes Shivam’s second statement true and so we know that Shivam is an alternator. Shivam does not own a cycle makes Ravi own a cycle. Shivam owns a Bike.

We conclude this post with this example where there are two alternators and one truth-teller. The question specifically mentions the number of truth-teller in order to avoid any ambiguity. Always look for Step 1 statements in order to make the task simpler and time saving and then go for the assumption-iteration method.