Time Trial on Trust
I have a selection of 4 fairly easy puzzles. You can do these in your head. Time yourself, and, if you dare – publish your time along with the answers. Read the questions carefully, and your time starts……. NOW!
1. 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 5 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours. What fraction of the tank (initially empty) will be filled in 1.35 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
2. The son of a rich bullion merchant left home on the death of his father. All he had with him was a gold chain that consisted of 98 links. He rented a place in the city center with a shop at the lower level and an apartment at the upper level. He was required to pay every week one link of the gold chain as rent for the place. The landlady told him that she wanted one link of the gold chain at the end of one week, two gold links by the end of two weeks, three gold links by the end of three weeks and so on. The son realized that he had to cut the links of the gold chain to pay the weekly rent. If the son wished to rent the place for 98 weeks, what would be the minimum number of links he would need to cut?
3. A cylinder 48 cm high has a circumference of 16 cm. A string makes exactly 4 complete turns round the cylinder while its two ends touch the cylinder’s top and bottom. How long is the string in inches?
4. My Dad has a miniature Pyramid of Egypt. It is 3 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 / 5) 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?