Solution

The banana has found its way into Bipin's tummy!

Let us first consider Anil's statements. If his first statement is false, then it follows that the other two statements are true. So, if the first statement is false then it implies that Anil has indeed eaten the banana. But the second statement, as we have noted, has to be true. The second statement says he has not eaten any banana since the last month. Now, how can Anil have eaten the banana, and yet not have eaten any banana since the last one month? Again, if Anil's first statement is false, then the third statement "Deepak ate the banana" also has to be true. This means that Anil ate the banana, and also Deepak ate the banana. This again is contradictory since we know only one boy is involved, Thus, Anil's first statement cannot be false; it has to be true. He is not the culprit.

We will consider Bipin's statements afterwards. Let's first consider Chandra statements. If Chandra has eaten the banana, his first statement is a lie and the other two statements are true. Thus, the statement that Deepak has taken the banana is true. The banana has been eaten by only one boy - both Deepak and Chandra are not culprits. Chandra's first statement is, therefore, true and he is not the culprit.

Let us consider Deepak's statements next. Suppose Deepak has eaten the banana, then his first statement is a lie and the other two statements are true. Therefore, the statement that Edwin has eaten the banana is true. As before we see that this is a contradiction because only one of the boys has eaten the banana. Thus, Deepak's first statement is true and he is not the culprit.

What about Edwin? The same reasoning holds here too. If Edwin has eaten the banana then his statement that Bipin has taken the banana, is true. This is not possible. So, Edwin is not the culprit.

That leaves only Bipin. He did see the bananas on the table, and he does feel scared to touch things that do not belong to him but his hunger was so great that he overcame his fright and gobbled up one banana.