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Infosys Placement Puzzles (Ten Puzzles completely solved )

Qn. 1 A frog fell into 30 mt deep well and tries to getout,it goes 3mts up and fall 2mts every day. we have to calculate no of days it take to getout.
Ans
1st day it rises 1 mt,2nd day 1 mt, like wise 27 day 27 mts but on 28th day by climbing 3 mts it gets out no change for sleep again So in 28 days it will get out of well

Qn. 2 There was a robbery happened at a bank and 3 suspects taken into custody.Their statements
    A:I am innocent
    B:I am innocent
    C:B did it.
   In these three one is lying and find the culprit.
Ans
if A lied
 complement of A (~A) and C contradicts so not possible
if B lied
 no contradiction on three statements A, ~B, C
if C lied
not possible to determine the culprit clearly becoz ~C only gives B did not done that, but no proof who done that
So the answer is B lied and B is Culprit

Qn. 3.A cube, which is painted red on all its sides, is cut into 27 cubes with three straight cuts. Now how many cubes have i)No red face ii)1 red face iii) 2 red faces iv) 3 red faces
Ans
Out of 27 small cubes there will be only one cube not in the big cube's face so only one cube not painted i.e no red faces
Of the remaining 26 cubes there will be only 6 cubes not in the edges so only painted on one face i.e 1 red face
Of the remaining 20 cubes there will be 8 cubes on the corner painted on three sides i.e 3 red faces
Remaining 12 which are in edges are painted in two sides i.e 2 red faces

Qn.4     XYZ         XYZ
       +AB        - AB
    ----------    ----------
      CDEF         BGA
     find the values of  X, Y, Z,G

Ans
Immediately by analysing Addition problem, we can say C = 1 because maximum possible carry by adding three digit number and two digit number is 1, also X = 9 because three digit number less than 900 will not give a four digit number by adding with two digit number in the same line D = 0 because even if the three digit number is 999 and two digit number is 99 we will not get 1100

also by analysing subraction problem
we can say immediately B = 8 because no three digit number in 900s will go to 700 by subracting two digit number
Analysing column wise the subraction problem
Z- 8 = A i.e Z = A+8 (it is not possible as only possible value for A is 1, othe than one will give two digit value for Z which is not allowed so A = 1 will give Z = 9 but 9 is alotted for X)
OR
10 + Z -8 = A i.e Z = A -2 so A may be 2,3,4,5,6,7
if A = 7 then Z = 5 that gives (Y-1+10-7)= G i.e Y +2 = G also two digit number in seventies so we want three digit number more than 920  that means Y may be 2,4
    if Y = 4 then G = 6 then you will get answer  
    if Y = 2 then G = 4 here this option fails in addition (two digits for same number)
answer is 945   945
             -78   +78
            867  1023 

Qn.5.There is a cycle race going on in a circular track and 1/5th of the total in front a person and 5/6th of the total behind that person gives up the total number of  participants. Total how many participants are there?
Ans
Let us take there are x persons
so other than him there are x-1 persons
x-1 persons are before and also behind the person as it is a circular race 
so
(1/5)(x-1)  + (5/6)(x-1) = x

31(x-1) = 30x
31x - 31 = 30x
that gives x = 31

Qn.7 A and B have the same number of marbles when they start playing. After some time A gains 20 marbles and later he loses 2/3rds of what he had. Now B has 4 times as many marbles as A has. What are the initial number of marbles that each of them had?
Ans
Intially let us take both had x marbles
after some time
A got x + 20 So B got x - 20
Again
A loses (2/3) of x+20 so B gained that Now B has x-20 + (2/3)(x+20)
which is equal to 4 times of A's marbles but now A has only (1/3) (x+20)
So by comparing we can say x- 20 = (2/3)(x+20)
that gives x-20 = 2x/3+ 40/3
that gives x = 100 

Qn.8.A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a  bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs?
Ans
x shoestrips 4x packet pins and 8x handkerchiefs
shoe strips cost x*x,packet pins cost 16 x*x  and handkerchiefs cost 64x*x
so totally 81 x*x equalls to 324 paise
x*x equals to 4
x = 2
that means 16 handkerchiefs (8x)

Qn.9. One person went to market to purchase three varieties of chocolates. He had purchased 20 items with 20 cents. Fudges are available at 4 cents each, chaco bars are available at 4 for a penny and gum pints are available at 2 a penny. How many of each item he had purchased.
Ans
x fudgets,y chaco bars and z gum pints ( Note : penny is nothing but cent)
fudgets cost 4x cents
chaco bars costs .25y
gum pints costs .5z

x+y+z = 20
4x+.25y+.5z= 20

So x can be 4 or 3 or 2 or 1
if x = 4 then .25y +.5z = 4 i.e  y + 2z = 16
so y/2 + z = 8
then y = 2 or 4 or 6 or 8 or 10 or 12 or 14 also z = 7 or 6 or 5 or 4 or 3 or 2 or 1 respectively
in none of the case y + z = 16 (i.e x+y+z= 20)

so if x = 3 then .25y +.5z = 8 i.e  y + 2z = 32
so y/2 + z = 16
then y = 2 or 4 or 6 or 8 or 10 or 12 or 14 ....also z = 15 or 14 or 13 or 12 or ...
but y = 2, z = 15 will give y+z = 17 i.e x+y+z = 20
So answer x = 3, y = 2, z = 15

Qn.10.There is a five digit number, where the third number is one higher than the sum of first and second digits. Fourth digit is twice of fifth and third digit is twice the fourth. Second digit is five more than the first digit. What is the number?
Ans
Let us take 'abcde' is the number

Given
c = a+b+1 ---(1)
d = 2e-------(2)
c = 2d-------(3)
b = a+5------(4)

(1) , (4) gives c = 2a+6  that means an even number more than 6 i.e 8
so d = 4 by (3) that means  e = 2 by (2) and also a = 1 and b = 6

The given number is 16842