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Sunday, 30 November 2014

The Egg Vendor and His Eggs

           Rasool, the man who delivers eggs to my home every day, did not turn up one day. So when he came the next morning I demanded an explanation from him. He told me the following story:

         The previous morning when he just came out of the house carrying a basketful of eggs on his head to start his daily rounds and stepped on to the street, a car going at full speed brushed against him and knocked down his basket destroying all the eggs. The driver, however, a thorough gentleman admitted his responsibility and offered to compensate him for damages. But Rasool could not remember the exact number of eggs he had, but he estimated the number between 50 and 100. He was also able to tell the gentleman that if the eggs were counted by 2’s and 3’s at a time, none would be left, but if counted by 5’s at a time, 3 would remain, and that he sold the eggs 50 paise a piece.

        The gentleman made some quick calculations and paid Rasool adequately.

          How much did the gentleman pay Rasool?

Answer:  The simplest way is to find those numbers between 50 and 100. Which are multiples of 2 and 3 leaving no remainder. These numbers are 54, 60, 66, 72,78,84,90 and 96. By scrutiny we find that if 78 are divided by 5 it will give 15 plus 3 left over. Therefore, 78 is the total number of eggs Rasool had in his basket, before the accident.
              And, therefore, he was paid Rs. 39 by the gentleman.

The Faulty Watch

       One day I found a strange thing happening to my watch- the minute hand and hour were coming together every sixty- five minutes. I decided to get it checked. 

        Was my watch gaining or losing time, and how much per hour?

Answer:     If 65 Minutes be counted on the face of the same watch then the problem would be impossible, because the hands must coincide every 65 ⁵⁄₁₁ minutes as shown by its face – and it hardly matters whether it runs fast or slow. However. If it is measured by actual time, it gains ⁵⁄₁₁ of a minute in 65 minutes or ⁶⁰⁄₁₄₈ of a minute per hour.

Pigs and Ducks

           While driving through the countryside one day I saw a farmer tending his pigs and ducks in his yard. I was curious to know how many of each he had. I stopped the car and inquired. Leaning on the stile jovially, he replied, ‘I have altogether 60 eyes and 86 feet between them’. 

           I drove off trying to calculate in my mind the exact number of ducks and pigs he had.    

         What do you think is the answer?

Answer:  There were sixty eyes, so there must have been thirty animals. Now the question is what combination of four- legged pigs and two- legged ducks adding to thirty will give 86 feet. With some pencil work, we get the answer 13 pigs and 17 ducks.

Problem from Lilavati

          Here is an ancient problem from Bhaskaracharya’s Lilavati:

          A beautiful maiden, with beaming eyes, asks me which is the number hat, multiplied by 3, then increased by three- fourths of the product, divided by 7, diminished  by one – third of the quotient , multiplied by  itself, diminished by 52, the square root found , addition of 8, division by 10 gives the number 2?
         Well, it sounds complicated, doesn’t it? No, not if you know how to go about it.

Answer:  28 is the answer.

The method of working out this problem is to reverse the whole process- multiplying 2 by 10, deducting 8. Squaring the result and so on.

Heads I win Tails I lose

           During my last visit to Vegas in the U.S.A. I met a man who was an inveterate gambler. He took out a coin from his pocket and said to me, ‘Heads I win tails I lose. I’ll bet half the money in my pocket.

          He tossed the coin, lost and gave me half the money in his pocket. He repeated the bet again and again each time offering half the money in his pocket. 

          The game went on for quite some time. I can’t recollect exactly how long the game went on or how many times the coin was tossed, but I do remember that the number of times he lost was exactly equal to the number of times he won.

          What do you think did he, on the whole, gain or lose?

Answer: The man must have lost. And the longer he went on the more he would lose – with simple calculations. We can draw this conclusion.

 In two tosses he was left with three quarters of his money.

In six tosses with twenty – seven sixty- fourths of his money, and so on.

Immaterial of the order of the wins and losses, he loses money, So long as their number is in the end equal.

Mathematics and Literature

          Recently a publishing company which specializes in mathematical books advertised the job opening of an assistant editor. The response was good. One hundred people applied for the position. The company, however, wanted to make their selection from the applicants who had some training in both mathematics and literature.

        Out of one hundred applicants the company found that 10 of them had no training in mathematics and no training in literature, 70 of them had got mathematical training and 82 had got training in literature.

        How many applicants had got training in both mathematics and literature?

Answer:   ten applicants had neither mathematics nor literature training. So, we can now concentrate on the remaining 90 applicants. Of the 90 .twenty had got no mathematics training and eight had got no –literary training.
That leaves us with a remainder of 62 who have had training in both literature and mathematics.

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