One night, three naughty boys stole a basketful of apple 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 1/3 of the rest, hid them separately and went back to sleep. Shortly thereafter, another boy awoke, counted the apples and he again found that if he took one for himself the loot could be divided into three equal parts. He ate up one apple, bagged 1/3 of the remainder, hid them separately and went back to sleep. The third boy also awoke after sometime, 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 1 more than could be divided into three equal parts. How many apples did the boy steal?
Answers
Boys steal 79 Apples
Step-by-step explanation:
Let say apple were = A A < 100
First one ate 1 apple & took one 3rd of remaining
so remaining apples = 2(A - 1)/3
Second one ate 1 apple & took one 3rd of remaining
so remaining apples = 2( 2(A - 1)/3 - 1)/3
= 2( 2A - 2 - 3)/9
= 2(2A - 5)/9
Third one ate 1 apple & took one 3rd of remaining
so remaining apples = 2 ( 2(2A - 5)/9 - 1)/3
= 2 ( 4A - 10 - 9 )/27
= 2( 4A - 19)/27
= (8A - 38)/27
(8A - 38)/27 = 3N + 1
=> 8A - 38 = 81N + 27
=> 8A = 81N + 65
A < 100 => 8A < 800 => N < 10
N = 7 A = 79 Satisfies this
Apples were 79
Boys steal 79 Apples
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