Story of Farmer's 3 Sons

A farmer’s wife made some chapatis…The farmer had 3 sons…. 

The first son came, gave one chapati to the dog,and made three equal parts of remaining chapatis, ate one part of it and left the other two parts for his brothers…. Other two sons came one after the other and did the same thinking that they came first…

Then at night all three came to the house, one of them gave one chapati to dog and made three equal parts and the three brothers ate one-one part of it… 

If no chapati was broken in pieces then how many minimum number chapatis did the mom made?

Here are MATHEMATICAL steps for solution! 

Mathematics in the Story of Farmer's 3 Sons

What was the story?

Let X be the number of chapatis that farmer's wife made.

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First son gave 1 chapati to dog. Chapatis left = (X - 1)

Made 3 equal parts of remaining. Chapatis in each part = (X - 1)/3

He Ate one part of it. Chapatis left = 2(X - 1)/3.

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Second son gave 1 chapati to dog. Chapatis left = 2(X - 1)/3 - 1

Made 3 equal parts of remaining. Chapatis in each part = [2(X - 1)/3 - 1]/3

He Ate one part of it. Chapatis left = 2[2(X - 1)/3 - 1]/3 

                                                  = [4(X-1) – 6]/9

                                                  = (4X - 10)/9

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Third son gave 1 chapati to dog. Chapatis left = (4x - 10)/9 - 1

Made 3 equal parts of remaining. Chapatis in each part = [(4X - 10)/9 - 1]/3

He Ate one part of it. Chapatis left = 2[(4X - 10)/9 - 1]/3

                                                  = (8X – 20 – 18)/27 
       
                                                  = (8X – 38)/27 

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At that night, one of them gave 1 chapati to dog.

Chapatis left = (8X – 38)/27 - 1

After that they made 3 equal parts of remaining parts and each son ate one part.

If we assume that each son ate Y chapatis then,

Y = [(8X – 38)/27 - 1]/3

Y = (8X - 38 – 27)/81

Y =  (8X – 65)/81

81Y= 8X - 65

X = (81Y + 65)/8 

X = 81Y/8 + 65/8

X = 10Y + Y/8 + 8 + 1/8

X = 10y + 8 + (y+1)/8

For X to be integer, Y has to be 7,15,23.....

So possible values of X are - 79, 160, 241.

Since, question asks minimum number, the farmer's wife must have made 79 chapatis in total.

Birbal The Wise!

Emperor Akbar once ruled over India. He was a wise and intelligent ruler, and he had in his court the Nine Gems, his nine advisors, who were each known for a particular skill. One of these Gems was Birbal, known for his wit and wisdom. 

The story below is one of the examples of his wit. Do you have it for you to find out the answer? 

A farmer and his neighbor once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbor, "and now he wants me to pay for the water." "That"s right, your Majesty," said the neighbor. "I sold him the well but not the water!" The Emperor asked Birbal to settle the dispute. 

Now it's very difficult to think what Birbal had in his mind at that time. Still you can give a try. How did Birbal solve the dispute? 

Read here how Birbal rescued the farmer! 

Source 

Justice WIth The Farmer

What's the story behind the title? 

"So you have sold the well to the farmer but not the water?" Birbal asked the neighbor. 

"Do you agree that owner of well is the farmer & you are owner of water?" Birbal asks further.

"Exactly!", neighbor replied.

Birbal now points towards the valid question - "So you need to pay rent for keeping your water in his well, or take out all of the water out of well. Don't you?"

By now the neighbor realized that he was outwitted. He had no option other than to apologize & take back his claim.

Fair Distribution of Farmer's Cows

What was the interesting?

First let's name 5 sons as A,B,C,D & E. Now look at the image below.

Just collect numbers surrounded by same shapes. If you observe carefully answer, a difference of 4 created at one place which is compensated at other 4. Each son would be getting 65 liters of milk.

Fair Distribution of Cows