Question

There are four friends they bought some bananas it's night they discussed to share early in the morning in night first friend silently i want my bananas now only and he divided the bananas into four equal parts then one is left he gave it to the monkey and the second friend also told that i want now only
bananas and divided again into four equal parts and again one banana left again gave to monkey third friend also wanted his bananas now only and divided into four equal parts again one banana left then gave to the monkey fourth friend also want his bananas now only and divided into four equal parts one banana is left gave to the monkey in morning they not told about each other and they divided into four equal parts there is no banana left to monkey this time.How many bananas did they bought?​

Answer 1

The total number of bananas they brought from Narendra's garden are 765 in number.  

Explanation :

Let the number of bananas were brought by them from Narendra's garden be 'X'  

From 'X', total number of bananas the first one took = (X -1)/4

We need to eliminate the banana he threw away.

Bananas remained are = X - ((X -1)/4 ) - 1  

                                     = ( 4X  - X  + 1 - 4) / 4

                                     = 3(X  - 1) / 4

Similarly, the no.of second one had took with him = (3/16)(3X  - 7)

the third one =  (3/64) (9X - 37)

the fourth one = (3/256)(27X  - 175)

Then, on talking 4 equal parts from the bananas left on the next morning, the share happened exactly. As in :

(3/256)(27X  - 175) = 4n

81X  - 525 = 1024n

81X  =  1024n + 525    ----------------- (1)

Here, n is the integer which we need to find.

(81 * 12n + 13 * 4n  + 81 * 6 + 13 * 3)/81

As per this statement, (4n+3)/81 is an integer. On solving,

4n + 3 = 81c  ; where c is a constant.

4n = 3 ( 27c -1 )

Let us check, on substituting which integer in c, the total value becomes a multiple of 4.

c = 0;  3(27(0)-1) = -3  (Incorrect)

c = 1;  3(27(1)-1) = 3(26)  (Incorrect)

c = 2;  3(27(2)-1) = 3(53)  (Incorrect)

c = 3;  3(27(3)-1) = 3(80)    (Suits!) As 80 is a mutiple of 4.

So, at c=3, we get

4n = 3(80)

n = 3(20)

n = 60

As n=60, substitute this value in eqn (1), As in :

81X = 1024 * 60 + 525

81X = 61440+ 525

X = 61965 / 81

X = 765

Therefore, the total number of bananas they brought from Narendra's garden are 765.  

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