Difficult Mathematical Puzzles - 5

Q.1. Stranded on a deserted island, Harry Puttar is left with only a 40 litres container of milk. To conserve his milk he decides that on the first day he will drink one litre of milk and then refill the container back up with water. On the 2nd day he will drink 2 litres and refill the container. On the 3rd day he will drink 3 litres and so on... By the time all the milk is gone, how much water has he drunk?

Q.2. A 3 digit number is such that its tens digit is equal to the product of the other two digits which are prime. Also, the difference between its reverse and itself is 99. What is the sum of the three digits?

Q.3. One side of the bottom layer of a triangular pyramid has 11 balls. How many are there in the whole pyramid? Note that the pyramid is equilateral and solid.

Q.4. Substitute numbers for the letters so that the following mathematical expressions are correct.

ZYX/3 = LQ, PQR/6 = LQ, JKL/9 = LQ

Note that the same number must be used for the same letter whenever it appears.

Q.5. When Poonia died, he willed his 17 dogs to the sons, to be divided as follows:

First Son to get 1/2 of the dogs, Second Son to get 1/3rd of the dogs & Third Son to get 1/9th of the dogs. The sons are sitting there trying to figure out how this can possibly be done, when a very old wise man goes riding by. They stop him and ask him to help them solve their problem. Without hesitation he divides the dogs properly and continues riding on his way. How did he do it?

Q.6. There are 3 colored boxes - Yellow, Black and Orange. Each box contains 2 envelopes. Each envelope contains cash - two of them contain Rs. 250000 each, two of them contain Rs. 150000 each and remaining two contain Rs. 100000 each.

There is one statement written on the cover of each box.

* Yellow Box: Both, a yellow box and a orange box contain Rs. 100000 each.

* Black Box: Both, a black box and a yellow box contain Rs. 250000 each.

* Orange Box: Both, a orange box and a black box contain Rs. 150000 each.

Only one of the above 3 statements is true and the corresponding box contains the maximum amount.

Can you tell which box contains the maximum amount and how much?

Q.7. There are 511 oranges and 9 empty boxes. An orange vendor asks his son to place all the 511 oranges in all the 9 boxes in such a manner that if he asks for any number of oranges from 1 to 511, his son should be able to pick them in terms of boxes. How did the son place all the oranges among the 9 boxes, given that any number of oranges can be put in one box?

Q.8. 100 Engineers and diploma holders were employed by company XYZ for a website designing task. The company did not allowed any lady engineer to work without her spouse who should also be an engineer. Also, atleast half the men engineers working came with their wives who are also engineers. The company paid five hundred rupees per day to each man engineer, four hundred rupees to each woman engineer and one hundred rupee to each diploma holder. the company gave out 20000 rupees every evening.

How many men engineers, women engineers and diploma holders were working with the company?

Q.9. A bag of Apricots was divided between Amitabh and Abhitabh. Abhitabh said, "It's not fair! You have 3 times as many Apricots I have." Amitabh said, "OK, I will give you one Apricot for each year of your age." Abhitab replied, "Still not fair. Now, you have twice as many Apricots as I have." "Dear, that's fair enough as I am twice older than you", said Amitabh. Amitabh went to Kitchen to drink juice. While he was in Kitchen, Abhitabh took apricots from Amitabh's pile equal to Amitabh's age. Who has more apricots now?

Q.10. Hansa ate a meal at Jugju hotel costing Rs.210. He gave the manager a Rs. 1000 note. He kept the change, came back a few minutes later and had some food packed for his girl friend 'Hansi'. He gave the accountant a Rs. 500 note and received Rs. 120 in change. Later the bank told the accountant that both the Rs. 1000 and the Rs. 500 notes were counterfeit.

How much money did the restaurant lose? Ignore the profit of the food restaurant.