poisoned bottle !!

u are the ruler of an empire and u are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. u have got thousand bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned...


The poison exhibits no symptoms until death. Death occurs within 10 to 20 hours after consuming even the minutest amount of poison..!!


u have over a 1000 slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.


You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.


What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

can u solve this??

This is a famous paradox which has caused a great deal of argument and disbelief from many who cannot accept the correct answer. Four balls are placed in a hat. One is white, one is blue and the other two are red. The bag is shaken and someone draws two balls from the hat. He looks at the two balls and announces that at least one of them is red. What are the chances that the other ball he has drawn out is also red?

why'd he do that ??

Two boys were playing on a tool shed roof when the roof collapsed with a crash. The boys fell uninjured to the floor below, but when they picked themselves up, the face of one boy was covered in dirt and the other boy's was still clean. Instantly, the boy with the clean face ran off to wash his face, while the one with the dirty face remained placidly behind. Why did the boy with the clean face act as he did?

important example problems to be noted

(1)Find the time taken by a train 180m long,running at 72kmph in 
crossing an electric pole


Solution:
          Speed of the train =72*5/18m/s =20  m/s
          Distance move din passing the pole = 180m
          Requiredtime = 180/20 = 9 seconds


(2)A train 140 m long running at 60kmph.In how much time will it
pass a platform 260m long.


Solution:
          Distance travelled =140 + 260 m =400 m,
          speed = 60 *  5/18 = 50//3 m
          time=400*3   / 50 = 24 Seconds




(3)A man is standing on a railway bridge which is 180 m.He finds 
that a train crosses the bridge in 20 seconds but himself in
8 sec. Find the length of the train and its sppeed


Solution:
         i)D=180+x
                   T = 20 seconds
               S= 180+x / 20  ------------ 1
         ii)D=x
                   T=8 seconds
                   D=ST
                   x=8S        -------------  2
            Substitute 2 in 1
                S=180 + 8 S  / 20
                S=15 m/s
        Length of the train,x is 8 *15 = 120 m




(4)A train 150m long is running with a speed of 68 mphIn wht 
time will it pass a man who is running at a speed of 8kmph in 
the same direction in which the train is going


Solution:
         Relative Speed = 68-8=60kmph*5/18 = 50/3 m/s
                    time= 150 * 3   /50 =9sec


5)A train 220m long is running with a speed  of 59 k mph /..In 
what time will it pass a man who is running at 7 kmph in the 
direction opposite to that in which train is going.


Solution:
          Relative Speed = 59+7=66kmph*5/18 = 55/3 m/s
                     time= 220/55 * 3 =12sec

important concepts for solving train problems..!!

General Concept: 


(1) Time taken by a train x mt long in passing a signal post
or a pole or a standing man = time taken by the train to cover x mt


(2) Time taken by a train x mt long in passing a stationary
object of length y mt = time taken by the train to cover x+y mt


(3) Suppose two trains or two bodies are moving in the same 
direction at u kmph and v kmph such that u > v then their 
relative speed is u-v kmph


(4)If two trains of length x km and y km are moving in opposite
diredtions at u kmph and vmph,then time taken by the train to
cross each other = (x+y)/(u+v) hr


(5) Suppose two trains or two bdies are moving in opposite direction
at u kmph and v kmph then,their relative speed = (u+v) kmph


(6)If two train start at the same time from 2 points A & B towards
each other and after crossing they take a & b hours in reaching B & A 
respectively then A's speed : B's speed = (b^1/2 :   a^1/2 )

where is the remaining dollar??

3 people check into a hotel. They pay $30 to the manager, and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy thinks that $5 would be difficult to share among 3 people... so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totaling $27. The bellboy has $2, totaling $29. Where is the remaining dollar?

Find at what time between 8 and 9 o'clock will the hands of a 
clock be in the same straight line but not together ?