Nuts for the Nuts

     Last time I visited a friend’s farm near Bangalore he gave me a bag containing 1000 peanuts. From this I took out 230 peanuts for myself and gave away the bag with the remainder of peanuts to three little brothers who live in my neighbourhood and told them to distribute the nuts among themselves in proportion to their ages- which together amounted to 17½ years.

   Thinku, Rinku and Jojo, the three brothers, divided the nuts in the following manner:

   As often as Tinku took four Rinku took three and as often as Tinku took six Jojo took seven. 

   With this data can you find out what were the respective ages of the boys and how many nuts each got?

Answer:  When Tinku takes 12, Rinku and Jojo will take 9 and 14, respectively – and then they would have taken altogether thirty- five nuts.

                  Thirty- five is contained in 770 twenty- two times which means all one has to do now is merely multiply 12, 9 and 14 by 22 to find that Tinku’s dhare was 264, Rinku’s 198 and Jojo’s 308.

                 Now as the total of their ages is 17½ years or half the sum of 12,9 and 14, their respective ages must be 6,4 ½ and 7 years.

Cotton or Gold

       Which would you say is heavier, a pound of cotton or a pound of gold?

Answer:  A pound of cotton is heavier than a pound of gold because cotton is weighed by the avoirdupois pound, which consists of 16 ounces, whereas gold, being a precious metal is weighed by the troy pound which contains 12 ounces (5760 grams).

The Counterfeit Note

       While walking down the street, one morning, I found a hundred rupee note on the footpath. I picked it up, noted the number and took it home.

      In the afternoon the plumber called on me to collect his bill. As I had no other money at home, I settled his account with the hundred rupee note I had found. Later I came to know that the plumber paid the note to his milkman to settle his monthly account, who paid it to his tailor for the garments he had made.

        The tailor in turn used the money to buy an old sewing machine, from a woman who lives in my neigh bourhood. This woman incidentally, had borrowed hundred rupees from me sometime back to buy a pressure cooker, remembering that she owed me hundred rupees, came and paid the debt.

          I recognized the notes as the one I had found on the footpath, and on careful examination I discovered that the bill was counterfeit.

         How much was lost in the whole transaction and by whom?

Answer:  All the transactions carried out through the counterfeit note are invalid, and, therefore, everybody stands in relation to his debtor just where he was before I picked up the note.

The Number and the Square

               In the diagram the numbers from 1to 9 are arranged in a square in such a way that the number in the second row is twice that in the first row and the number in the bottom row three times that in the top row.

               I am told that there are three other ways of arranging the numbers so as to produce the same result.

 Can you find the other three ways?

1            9                2

3            8                4

5            7                 6

Answer: While the first was the example given, the top row must be one of the four following numbers: 192.219.273 or 327.

Something for the Marmalade

       A little girl I know sells oranges from door to door.

One day while on her rounds she sold ½ an orange more than half her oranges to the first customer. To the second customer she sold ½ an orange more than half of the remainder and to the third and the last customer she sold ½ an orange more than half she now had, leaving her none.

       Can you tell the number of oranges she originally had? Oh by the way she never had to cut an orange.

Answer:  In order that the little girl should have disposed of the oranges she had remaining after her second sale, she must have had at least one whole orange remaining so that she could deduct from it ‘half of her oranges plus half an orange’, for the third and the remaining so that she could deduct from it’ half of her oranges plus half an orange represents half of the remaining after the second sale, then she must have sold two oranges in her second sale. Leaving the 3 oranges after the first sale.

Lastly, if three oranges only represent half the original number, plus half an orange, then she must have started with [(3 ×2) + 1] or 7 oranges.