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 ?

Compound Interest

Important Facts and Formulae: 


Compound Interest: 
Sometimes it so happens that the borrower and the lender 
gree to fix up a certain unit of time ,say yearly or 
half-yearly or quarterly to settle the previous account.
In such cases ,the amount after the first unit of time 
becomes the principal for the 2nd unit ,the amount after
second unit becomes the principal for the 3rd unit and so
on. After a specified period ,the difference between the 
amount and the money borrowed is called Compound Interest
for that period.


Formulae:


Let principal=p,Rate=R% per annum Time=nyears


1.When interest is compounded Annually,
Amount=P[1+(R/100)]n
2.When interest is compounded Halfyearly,
Amount=P[1+((R/2)100)]2n
3.When interest is compounded Quaterly,
Amount=P[1+((R/4)100)]4n
4.When interest is compounded Annually,but time in fractions
say 3 2/5 yrs Amount=P[1+(R/100)]3[1+((2R/5)/100)]
5.When rates are different for different years R1%,R2%,R3%
for 1st ,2nd ,3rd yrs respectively
Amount=P[1+(R1/100)][1+(R2/100)][1+(R3/100)]
6.Present Worth of Rs.X due n years hence is given by 
Present Worth=X/[1+(R/100)]n

What is the sum of all numbers between 100 and 1000 which are 
divisible by 14?

A railway track runs parallel to a road until a bend brings the road
to a level crossing. A cyclist rides along to work along the road 
every day at a constant speed of 12 miles per hour.
He normally meets a train that travels in the same direction at the 
crossing One day he was late by 25 minutes and met the train 6 miles 
ahead of the level crossing. Can you figure out the speed of the train?

Boat problems

Important facts:  


1)In water, the direction along the stream is called down stream.


2)Direction against the stream is called upstream.


3)The speed of boat in still water is U km/hr and the speed of 
stream is V km/hr then 


speed down stream =U + V km/hr
speed up stream = U – V km/hr


Formulae:


If the speed down stream is A km/hr and the speed up stream is 
B km/hr then speed in still water = ½(A+B) km/hr
rate of stream =1/2(A-B) km/hr


Problems:


1. In one hour a boat goes 11 km long the stream and 5 km 
against the stream. The speed of the boat in still water is?


Sol:
       Speed in still water = ½ ( 11+5) km/hr= 8 kmph


2.A man can row 18 kmph in still water. It takes him thrice 
as long as row up as to row down the river. find the rate 
of stream.


Sol:
       Let man's rate up stream be xkmph
    then, in still water =1/2[3x+x]=2x kmph
             so, 2x= 18, x=9
          rate upstream =9kmph
         rate downstream =27 kmph
         rate of stream = ½ [27-9]
                        = 9kmph


3.A man can row 71/2kmph in still watre . if in a river 
running at 1.5 km an hour, if takes him 50 min to row to 
place and back. how far off is the place? 


Sol:        speed down stream =7.5+1.5=9kmph
               speed upstream =7.5-1.5=6kmph
          let the required distence x km. then ,
          x/9+x/6=50/60 = 2x+3x= 5/6*18
                 5x=15,     x=3
         Hence, the required distence is 3 km


4.A man can row 3 quarters of a km aganist the stream is
111/4 min. the speed of the man in still water is ?


Sol: rate upstream = 750/625 m/sec =10/9 m/sec
       rate downstream =750/450 m/sec = 5/3 m/sec
     rate in still water =1/2[10/9+5/3] = 25/18 m/sec
                        = 25/18*18/5=5 kmph


5.A boat can travel with a speed of 13 kmph in still water.
if the speed of stream is 4 kmph,find the time taken by
the boat to go 68 km downstream?


Sol: Speed down stream = 13+4= 17 kmph
    time taken to travel 68km downstream =68/17 hrs
                              = 4 hrs
                                              Top


6.A boat takes 90 min less to travel 36 miles downstream then 
to travel the same distence upstream. if the speed of the 
boat in still water is 10 mph . The speed of the stream is :


Sol: Let the speed of the stream be x mph .
      then, speed downstream = [10+x]mph
          speed upstream =[10-x] mph
     36/[10+x] - 36/[10-x] = 90/60 =72x*60= 90[100-x2]
             (x+50)(x-2) =0
              x=2 kmph
7.At his usual rowing rate, Rahul 12 miles down stream in a 
certain river in 6 hrs less than it takes him to travel the
same distence upstream. but if he could double his usual 
rowing rate for his 24 miles roundthe down stream 12 miles 
would then take only one hour less than the up stream 12 miles.
what is the speed of the current in miles per hours?


Sol: Let the speed in still water be x mph and the speed of 
    the curren be y mph.
         then, speed upstream = (x-y)
         speed downstream =(x+y)
         12/(x-y) - 12/(x+y) = 6
     6(x2 – y2) m= 2xy => x2 – y2 =4y -(1)
    and   12/(2x-y) - 12/(2x+y) =1 => 4x2 – y2 = 24y
          x2= ( 24y + y2)/4 -->(2)
         from 1 and 2 we have
         4y+ y2 =( 24y+y2)/4 
           y=8/3 mph
           y= 22/3 mph

8.There is a road beside a river. two friends started from 
a place A, moved to a temple situated at another place B 
and then returned to A again. one of them moves on a cycle 
at a speed of 12 kmph, while the other sails on a boat at a
speed of 10 kmph . if the river flows at the speedof 4 kmph,
which of the two friends will return to place A first ?


Sol: Clearly, The cyclist moves both ways at a speed of 12 kmph
so, average speed of the cyclist = 12 kmph 
the boat sailor moves downstream = (10+4) = 14 kmph
upstream =(10-4) = 6 kmph
So, average speed of the boat sailor =[ 2*14*6]/[14+6] kmph
=42/5 kmph =8.4 kmph
Since, the average speed of the cyclist is greater, he will 
return to A first.


9.A boat takes 19 hrs for travelling downstream from point A to
point B. and coming back to a point C midway between A and B.
if the velocity of the sream is 4 kmph. and the speed of the 
boat in still water is 14 kmph. what is the distence between 
A and B?


Sol:
speed downstream =14+4 =18 kmph
speed upstream = 14 -4 = 10 kmph
let the distence between A and B be x km. then,
x/18 + (x/2)/10 = 19
x/18 + x/20 =19
19x/180 =19 =>x = 180km
Hence, the distence between A and B bw 180 km

If you look you cannot see me. And if you see me
you cannot see anything else. I can make anything you want happen, but 
later everything goes back to normal. What am I?

A man was found dead out in a field of snow. The 
only tracks that were left was a set of footprints between two parallel 
lines. Who should the police be looking for?

Important Facts: 


1.If A can do a piece of work in n days, then A's 1 day work=1/n 


2.If A's 1 day's work=1/n, then A can finish the work in n days.


Ex: If A can do a piece of work in 4 days,then A's 1 day's work=1/4.
    If A's 1 day’s work=1/5, then A can finish the work in 5 days 


3.If A is thrice as good workman as B,then: Ratio of work done by
A and B =3:1. Ratio of time taken by A and B to finish a work=1:3

A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8
days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract?
A. 7
B. 8
C. 11
D. 12

What is the maximum number of half-pint bottles of cream that can be filled with a 4-gallon can of cream (2 pt. =1 qt. and 4 qt. =1 gal)
A.16
B.24
C.30

D.64

can u?

Can you name four days which start with the letter 'T'?

solve this if u can !!

One snowy night, Sherlock Holmes was in his house sitting by a fire. All of a sudden a snowball came crashing through his window, breaking it. 
Holmes got up and looked out the window just in time to see three neighborhood kids who were brothers run around a corner. Their names were John Crimson, Mark Crimson and Paul Crimson.
The next day Holmes got a note on his door that read '? Crimson. He broke your window.'
Which of the three Crimson brothers should Sherlock Holmes question about the incident?

what day is it??

One day Alice meets the Lion and the Unicorn in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Unicorn, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Alice:
Lion: Yesterday was one of my lying days.
Unicorn: Yesterday was one of my lying days too.
What day is it?

try this out

The below is a number puzzle. It should be read left to right, top to bottom.
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
? ? ? ? ? ?
? ? ? ? ? ? ? ?

Question 1: What is the next two rows of numbers?
Question 2: How was this reached?

standard one

Outside a room there are three light switches. One of switch is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.


You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)


Your task is to then determine which switch controls the bulb ??