Difficult Mathematical Puzzles - 2

Mathematics puzzle questions are often asked in competitive exams and entrance tests. These are mostly arithmetic or algebra puzzles that test you on the basics of time, speed & distance, probability, clocks, etc. Here, we have compiled a variety of mathematics puzzles in three groups: easy, medium and difficult puzzles. Each article contains a set of 10 questions with solutions. In this article, you will come across difficult maths puzzles with answers and explanations.
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Solve the given questions and check your mental aptitude:
Q.1. The house number in Raja Karorimal lane starts with natural numbers, i.e. 1,2,3….. Sum of all the house numbers on the left side of Raja's residence in that lane is equal to the sum of all the house on its right side. There are more but less than 3000 houses on the right side of Raja's residence.
Q. What is my house number?
  1. 204
  2. 6929
  3. 288
  4. 7014
Q.2. The house number in Raja Karorimal's lane starts with natural numbers, i.e. 1,2,3….. Sum of all the house numbers on the left side of Raja's house is equal to the sum of all the house on its right side. There are more but less than 3000 houses on the right side of Raja's house.
How many houses are there in the lane?
  1. 9885
  2. 288
  3. 9801
  4. Data inadequate
Q.3. If ABC are distinct single digit natural numbers satisfying.
ABC
+ ACB
_______
BCA
Find the Values of A, B, C.
Q.4. Seth SS and the Seth JS were partners, in a business for many years. JS's share in the business was three-fifths as large as that of SS. As both were aging. They agreed to take in as a partner SS's son-in-law, Chottu. Chottu agreed to pay them Rs. 8,00,000 with the condition that after he became a partner, everybody should own exactly one-third of the business.
"I suppose the bulk of this amount will go to my father-in-law” said Chottu. "Why will it not be the whole amount?" exclaimed SS. "What do you mean?" retorted JS, "it has to be divided in the proportion of our share of profit."
How should this amount of Rs. 8,00,000 be shared?
Q.5. "Today my age is equal to the last two digits of my year of birth." said a boy to his grandfather in 1942. To this, his grandfather, with a chuckle, said," it is true in my case also." The boy was trying to figure out how. Will you explain?
Q.6. Peter and his son Repeter go around a track formed by an equilateral triangle. Peter's running speed is 5 mph and his walking speed is 1mph. Repeter' s walking and running rates are four times that of his father. Both start together from one vertex of the triangle, the son going clockwise & the father going anti-clockwise. Initially Peter runs and Repeter walks but thereafter, as soon as the father starts walking, the son starts running and both complete the course in 80 minutes.
For how long does Peter run? Where do the two cross each other?
Q.7. A diamond worker has been contracting for 15 months with a diamond merchant. The merchant told him that he would be getting one diamond each month from a diamond chain with 15 diamonds . However, he can break only three links in the first month. He cannot break any more links after the first month. Which three links should he break up in order to be able to get one diamond each month?
Q.8. If only 2 couples are existing today. Suppose each of these couple give birth to 4 children & the 8 children form 4 couples & each couple in turn give birth to 4 children, & those 16 form 8 couples & give birth to 4 children each & so on, can you tell exactly the number of persons existing after 10 generations, excluding the two initial couples?
Q.9. Out of two coins, one is fair (the probability of getting head is 1/2) and the other is biased with probability of getting a tail 1/3. One of the coins is tossed once, resulting in heads. The other is tossed three times, resulting in two heads. Which coin is more likely to be the biased one?
Q.10. A clock gains 2% time during the first week and then loses 2% time during the next one week. If the clock was set right at 12 noon on a Wednesday, what will be the time that the clock will show exactly 14 days from the time it was set right?
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