# A bowl of sweets was placed on a table to be distributed among three brothers rajan, sajal and karan. rajan arrived first and ate what he thought was his share of sweets and left. then, sajal arrived. he thought that he was the first one to arrive and ate the number of sweets, he thought was his share and left. lastly, karan arrived. he again thought he was the first one to arrive and he took what he thought was his share. if 16 sweets are left in the bowl finally, how many sweets did the bowl contain initially?

As mentioned in the question:

3 boys ate one-third of the sweets.

Now let us consider the initial number of sweets to be

(3 * 3 * 3)x = 27x

The sweets taken by Rajan =

$$\begin{array}{l}frac{1}{3}\end{array}$$
* 27x = 9x

Now the number of sweets left are 18x

The sweets taken by Sajal =

$$\begin{array}{l}frac{1}{3}\end{array}$$
* 18x = 6x

Now the number of sweets left are 12x

The sweets taken by Karan =

$$\begin{array}{l}frac{1}{3}\end{array}$$
* 12x = 4x

Now the number of sweets left are 8x

= 8x = 16 or x = 2

Therefore, the total number of sweets in the bowl is

= 27x = (27 * 2) = 54

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