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.