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One night three naughty boys stole a basket full of apples from the garden, hid the loot and went to sleep. Before retiring they did some quick counting and found that the fruits were less than a hundred in number. During the night one boy awoke, counted the apples and found that he could divide the apples into three equal parts if he first took one for himself. He then took one apple, ate it up and took $$\frac{1}{3}$$ of the rest, hid them separately and went back to sleep. Shortly thereafter another boy awoke, counted the apple and he again found that if he took one for himself the loot could be divided in to three equal parts. He ate up one apple, bagged $$\frac{1}{3}$$ of the remainder, hid them separately and went back to sleep. The third boy also awoke after some time, did the same and went back to sleep. In the morning when all woke up, and counted apples, they found that the remaining apples again totaled I more than could be divided into three equal parts. How many apples did the boys steal?
We'll approach this question by checking the options.
When the 1st boy woke up, he ate 1 and hid a third of the remaining, which leaves two-thirds.
So, if the initial no. of apples was N, after the actions of the 1st boy who woke up, now remaining apples are:
The 2nd boy repeats the process which makes the remaining no. of apples :
Now the 3rd guy repeats the process as well. No. of apples remaining after the 3rd operation:
Now this number has to be an integer and one less than this will be divisible by 3.
On putting the value of N as 67, 79 and 85 we can observe that only 79 satisfies the conditions.
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