History, asked by mk554488, 10 months ago

There will be four friends. Thieves are not thieves. All four bring some banana fruits together from the garden. Into the garden far home. Darkness drops by arrival. Well, the bananas will be Shared later in their room. 1. After a while, one gets up and I now feel like I'm taking my part, and the banana fruit is made up of four parts. One is left. He throws it out for a monkey and takes his share. 2. If the second person gets up and again make four parts of what is there, one will be left. He throws the one into the monkey and takes his part. 3. If the third person rises and the remaining four parts again, one will remain. He throws it to the monkey and takes his part. 4. If the fourth person rises and the remaining four parts again, one will be left again. He throws it to the monkey and takes his part. Dawn. Everybody will come. They never tell anyone what they have done. The four parts of the silent are captured by anyone. This time the monkey could not survive. So how many bananas are brought from the garden? fuzzle

Answers

Answered by poojan

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

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