Medium Mathematical Puzzles - 1

Mathematical Puzzles form an essential part of many competitive exams. One of the most commonly asked questions is based on arithmetic puzzles. Another important type of question features in form of number puzzles. Here is a compilation of the various types of medium-level mathematical puzzles with answers and explanations. Each article features a set of 10 math brain teasers to evaluate your level of preparation. 

Practice these mathematical puzzles and check your aptitude:

Q.1. In a swimming competition that went on for n successive days (n>1), m medals were awarded.

1. medal and 1/9 of the remaining (m – 1) medals were awarded on the first day.
2. medals and 1/9 of the now remaining medals was awarded on the second day; and so on
3. The remaining n medals were awarded, on the nth and last day.
   If same number of medals were awarded daily, how many days did the contest last, and how many medals were awarded altogether?
   
   Total 64 medals were awarded and the contest was for 8 days.
   On day 1: Medals awarded = (1 + 63/9) = 8 : Remaining 56 medals
   On day 2: Medals awarded = (2 + 54/9) = 8 : Remaining 48 medals
   On day 3: Medals awarded = (3 + 45/9) = 8 : Remaining 40 medals
   On day 4: Medals awarded = (4 + 36/9) = 8 : Remaining 32 medals
   On day 5: Medals awarded = (5 +27/9) = 8 : Remaining 24 medals
   On day 6: Medals awarded = (6 + 18/9) = 8 : Remaining 16 medals
   On day 7 : Medals awarded = (7 + 9/9) = 8 : Remaining 8 medals
   On day 8, the remaining 8 medals are awarded  
4. Q.2. There is banana shake in yellow colored glass and apple juice in a white colored glass, both containing equal volumes of shake and juice. 100ml of banana shake is taken and poured into the white glass. After that similarly, 100 ml from the white glass is poured into the yellow glass. Of the two quantities, the amount of apple juice in the yellow glass and the amount of banana shake in the white glass, which one is greater and by how much?
5. The two quantities are equal.
   Let's assume that both glasses contain 900 ml of liquid each. Now, 100ml of the banana shake is taken and poured into the White glass. Hence, yellow colored glass contains 800 ml of banana shake and white glass contains 900 ml of Apple juice and 100 ml of banana shake i.e. total of 1000 ml. Similarly, 100 ml of juice from white glass is poured into yellow glass. Now this 100 ml is not a pure apple juice. It contains 90 ml of apple juice and 10 ml of banana shake. Hence, yellow glass contains 810 ml of banana shake and 90 ml of Apple juice. Similarly, white glass contains 810 ml of apple juice and 90 ml of banana shake.
   Now it is clear that the amount of apple juice in the yellow glass and the amount of banana shake in the white glass are the same.