# Medium Mathematical Puzzles - 3

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Maths puzzle questions are often asked in a number of competitive exams. Most of the questions are based on arithmetic or number puzzles. Some of the riddles test your basics of clocks, profit-loss, probability, time, speed and distance. Here is a compilation of medium level maths puzzles with answers. You will be able to solve the concept based questions in form of algebra puzzles. Each article consists of 10 questions.
Solve the given questions and check your level of preparation:
Q.1. Solve the image
1. 125
2. 185
3. 156
4. 625
Clearly, ( 52-32 )= 16, ( 122-82 )= 80, ( 342-272 )= 427,So missing number is: ( 212-162 )= 185,. So answer is (b) option.
Q.2. If a shopkeeper gives 25% discount, he still earns 25% profit. If he now gives 10% discount then what is the profit percentage he gains?
Marked Price=100
After discount price = 75
Profit is 25% so Cost price = 60
If they give 10% discount, then Price = 90
Profit % = (30/60) x 100 = 50%
Q.3. There are as many four-legged chairs and as many four-legged tables as workers in the office of Yamraj, and as many three-legged stools as four-legged almirahs. If the number of stools be one more than number of workers and the total number of legs be 585,then what is the number of workers in the office?
4 legged chairs = 4 legged tables = number of workers.
3 legged stools = 4 legged almirahs
No. of stools = 1 + no. of workers
Total no. of legs = 585, Let the total number of workers= x.
2x + x × 4 + (x+1) 3 + (x+1) 4 = 585....x = 34.
Thus number of workers are 34.
Q.4. The diagram is a ‘ magic square’ in which all rows and columns and both diagonals add Up to 38. Find pq
 2 9 14 13 15 5 p 17 q 16
 2 9 14 13 15 12 3 8 5 6 17 10 16 11 4 7
So answer is 6×10 = 60.
Q.5. At 8:20 A.M., through how many degrees the hour hand of a clock moved since midnight?
After midnight at 9.00 A.M. Movement = 30×8 = 240°. In 20 minutes movement = 20x30/60 = 10° Total= 240° + 10° = 250°.
Q.6. One morning at sunrise one hiker begins to walk up a hill on a narrow path that spirals around it from the bottom all the way up to the top. Of course, he walks with varying speed, taking breaks to rest and to eat his lunch. He reaches the top of the hill in the evening, spends the night in a tent, and then, in the morning, starts to walk back down along the same path. By the sunset he reaches the bottom of the hill. Note, that his speed on the way down is greater than his speed on the way up. Prove that there is a spot along the path that the hiker will occupy on both trips at precisely the same time of day.
Imagine two people walking along the path toward each other at the same time (one from the top of the hill, the other one from the bottom). Obviously, they must meet somewhere along the way.
Q.7. In a grid of numbers, which will be greatest: the greatest of the smallest numbers in each column, or the smallest of the greatest numbers in each row?
Smallest of the greatest will be greater than greatest of the smallest. Consider number X who is at the intersection of the column with the greatest of the smallest (G), and the row with the smallest of the greatest (S). Clearly, S ≥ X ≥ G (the equality will happen if the smallest of the greatest is the same number as the greatest of the smallest). Therefore, S > T.
Q.8. A number can be constructed from any date of the year by adding the number of the month to the number of the day. For example: November 22nd would become the number 33, since November is the eleventh month, and 22 + 11 = 33. May 14 would become 19, and so on. How many different numbers can you make, using dates of the normal calendar?
Following is the list of the numbers that can be constructed each month.
January: 2 to 32 (From 1st January - 31st January)
February: 3 to 30 (From 1st February - 28th February)
March: 4 to 34 (From 1st March - 31st March)
April: 5 to 34 (From 1st April - 30th April)
May: 6 to 36 (From 1st May - 31st May)
June: 7 to 36 (From 1st June - 30th June)
July: 8 to 38 (From 1st July - 31st July)
August: 9 to 39 (From 1st August - 31st August)
September: 10 to 39 (From 1st September - 30th September)
October: 11 to 41 (From 1st October - 31st October)
November: 12 to 41 (From 1st November - 30th November)
December: 13 to 43 (From 1st December - 31st December)
Total 42 numbers are possible, every number between 2 and 43 inclusive
Q.9 In a casino, Anurag bets on number 23 on a spinning wheel 12 times and loses each time. On the 13th spin he does a quick calculation and finds out that the number 17 had appeared three times in the last 12 spins and is therefore, unable to decide whether to bet on 23 or 17 in the 13th spin. Which number (23 or 17) will give him the best chance of winning and what are the odds of winning on the bet that he takes? (Wheel has numbers 1 to 36)
1. 23; 2:1
2. 17; 19:17
3. Either; 18:1
4. Either; 35:1
Since each of the spin is an independent event, thus the outcome of the 13th spin will not depend on the outcome of the previous spins. Hence, the odds of winning on the number that Anurag bets on, is 35 : 1 in each case.
Q.10. The LAZY express runs between P & Q. For the up as well as the down journey, the train leaves the starting station at 6 AM everyday & reaches its destination at 7 AM after 3 days. Mr. Jain once traveled by Lazy Express from Q to P. How many trains by the same name did he cross en route?
Mr. Jain crosses exactly seven trains on the route - 3 trains which had already started before the start of Mr. Jain while 4 trains will be those which started after the start of Mr. Jain.
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