Amar, Bhavan and Chetan have a total of 40 marbles among them. First, Amar tripled the number of marbles with each of the other two by giving them some marbles. Next, Bhavan similarly triples the number of marbles with each of the other two. If Bhavan finally has 10 marbles, find the number of marbles he had initially.

This problem can be solved by working backwards from the final state of the marbles.

Step 1: We know that Bhavan finally has 10 marbles.

Step 2: Before Bhavan tripled the number of marbles with Amar and Chetan, he must have had a third of his final amount. So, Bhavan had 10/3 = 3.33 marbles. However, since the number of marbles must be a whole number, we can infer that Bhavan must have given away a fraction of a marble. This is not possible, so there seems to be a mistake in the problem.

The problem as stated does not have a solution in whole numbers.

This problem can be solved by working backwards from the final state to the initial state.

Step 1: Bhavan ends up with 10 marbles after tripling the number of marbles with Amar and Chetan. This means that before this transaction, Bhavan had 10/3 = 3.33 marbles. However, since the number of marbles must be a whole number, this is not possible.

There seems to be a mistake in the problem. The number of marbles Bhavan ends up with should be a multiple of 3 for the problem to be solvable.

This problem can be solved by working backwards from the final state to the initial state.

Step 1: Bhavan ends up with 10 marbles after tripling the number of marbles with Amar and Chetan. This means that before this transaction, Bhavan had 10/3 = 3.33 marbles, which is not possible since the number of marbles should be an integer.

Therefore, there seems to be a mistake in the problem as it is not possible for Bhavan to have a non-integer number of marbles. Please check the problem again.