Difficult Mathematical Puzzles - 4

Mathematical games and puzzles are based on the basic concepts of algebra, arithmetic, ratio & proportion, time & distance, probability, etc. Here is a compilation of different mathematical puzzles with solutions, grouped according to the level of difficulty. This article contains a set of 10 algebra based and arithmetic puzzles with answers. In this set, you will come across difficult mathematical puzzles devised to hone your mental aptitude.
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Solve these questions and check your level of preparation:
Q.1. A number of 5 digits have the following properties:
The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, . Each digit in the number is different i.e. no digits are repeated. The digit 0 does not occur in the number i.e. it is comprised only of the digits 5-9 in some order. How many such numbers are possible and find their value/values?.
Q.2. Power went off when Vijay was studying. It was around 2:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last four hours and the thin one one hours less. When he finally went to sleep, the thick candle was twice as long as the thin one. For how long did Vinay study in candle light?
Q.3. Rohit kanwar went to Bulls Eye bank to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither Rohit nor the cashier noticed that. After spending 23 paise, Rohit counts the money. And to his surprise, he has double the amount he wanted to withdraw. Find X and Y. (1 Rupee = 100 Paise)
Q.4. Find all sets of consecutive integers that add up to 1000.
Q.5. Lala Kirorimal's locker has a 5 digit number as the key. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11. Find the number.
Q.6. Consider a number 268, where last digit is the sum of first two digits i.e. 2 + 6 = 8. How many such 3-digit numbers are there?
Q.7. There is a 50m long soldier’s unit advancing forward. The last individual in the unit desires to give a letter to the foremost person leading the unit. So while the unit is marching he runs to the front, reaches the foremost person and hands over the letter to him and without stopping, he runs and comes back to his original position. In the mean time the whole unit has moved ahead by 50m. How much distance did the last person cover in that time? Assume that he ran the whole distance with uniform speed.
Q.8. Ram says to Sham, "Can you figure out how many Eggs I have in my bucket?" He gives 3 clues to Sham: If the number of Eggs I have
I) is a multiple of 5, it is a number between 1 and 19
II) is not a multiple of 8, it is a number between 20 and 29
III) is not a multiple of 10, it is a number between 30 and 39
How many Eggs does Ram have in his bucket?
Q.9. There are four clustors of Oranges, Apricots and Bananas as follows:
Clustor I : 1 Orange, 1 Apricot and 1 Banana
Clustor II : 1 Orange, 5 Apricot and 7 Bananas
Clustor III : 1 Orange, 7 Apricots and 10 Bananas
Clustor IV : 9 Oranges, 23 Apricots and 30 Bananas
Clustor II costs Rs 300 and Clustor III costs Rs 390.
Can you tell how much does Clustor I and Clustor IV cost?
Q.10. 1000 cats were kept under observation to check their growth rates. After six months, there were 1000R cats. At the beginning of the 3rd year, there were roughly 2828R cats, which was 4 times what the scientists placed in there at the beginning of the 1st year. If R is a positive variable, how many cats would be there at the beginning of the 11th year?
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