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.
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?
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?
Q.3. A positive integer that, when added to 2000 gives a sum which is greater than when multiplied by 2000. Find the positive integer.
Q.4. I was inquisitive and asked Mr. Dhaliwal about his birthday. With a mischievious smile on his face he replied. "The day before yesterday I was 96 years old and next year I will be 99." Assume that the current year is 2010, can you figure out the date of birth of Mr. Dhaliwal? .
Q.5. Everyday in his business Prakash had to weigh amounts from 1 kg to 364 kgs, to the nearest kg. What is the minimum number of different weights required and how heavy should they be?
Q.6. If Kumbkaran eats 60 pounds of rice every day EXCEPT every 7th day on which he only eats 50 pounds of rice. If he continues this, how many pounds of rice will he eat in 150 days?
Q.7. Which of the following set would contain the most 4's that when added together will sum the most ?
999 - 778, 777 - 556 or 555 - 333?
Q.8. You have a balance and the following weights: 4kg, 8kg, 16kg, 32kg, and 64kg. How many different possible weights can you measure with these items?
Q.9. 2 crates are being used to carry six boxes. Each crate can carry a maximum of 50 kg. The total weight of the boxes is 100kg:
30 kg, 26kg, 20 kg, 16 kg, 4 kg, 4kg,
In how many different ways can these boxes be packed into the crates?
Q.10. Mr. Sahil runs the Bulls Eye Bank.
You have to help him, though, because he has forgotten the combination number of the safe of the bank. Fortunately, he does remember some things about the number which may help you to help him.
  • The number has four digits (eg.1234 or 9876).
  • All the digits are different.
  • It begins and ends with an odd number and has two even numbers in the middle.
  • 19 and 519 divide it exactly.
What is the number which will open the safe?