Tag: math & puzzles

A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?" After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 2 hours to fill the tank with the large inlet pipe. On the other hand, it takes 4 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 6 hours. What fraction of the tank (initially empty) will be filled in 0.86 hours if all three pipes are in operation?

My Dad has a miniature Pyramid of Egypt. It is 4 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 2) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough. If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.