Infosys Puzzle

hi friends ,
plz solve these ..i need it urgently.......
1.One jar A contains half of wine Another jar B which is double in size of A contains 1/4 th of wine
Both r flled with water and pour into another jar.Whats the ratio of water and wine in third jar
2. If u were to plant trees in a square field of side 100ft such that the distance between each tree is atleast 10ft, how many trees can u plant?u can plant trees even on the boundaries -3 marks.
3 Two friends A and B had soiled cuffs and collars to be given to the laundry. The total no. of cuffs and collars were 30. After a week A gets back half the no. of cuffs and one third of the collars and pays 27cents. If cost of 4 cuffs equals the cost of 5 collars what is the amount payed by B for the remaining? -4 marks
4.There is a group of friends which sets out on a trip. Every day they travel 20 km more than the previous the day. At the end of trip which lasted for nine days they had covered a total distance of 1080 km.
a. How many kms did they travel on the 4th day?
b. How many kms did they travel on the last day? (Total 5 marks)
5 Two guys A and B are asked to tell a number between 1 and 1000 (ie.including 1 and 1000). What is the probability that B tells a number which is greater than the number told by A? -
6. A certain watch gains half a minute in the night and by dawn loses one third of a minute ie gaining one-sixth of a minute in a whole day. If the watch shows the right time on the 1st of May by what date would it become 5 minute fast?
7. The score of a particular test was calculated using the formula S=30+4C-W where 30 was the total no of questions adn C is the no. of correct answers and W is the no. of wrong answers. A student could leave a question and would not be penalized for that. A tells B that he has a score > 80. B was able to guess the exact score.For any other score other than the one guessed by B, which was still >80, B would not have been able to guess the no. of correct answers. What was exact no. of correct answers that A had got?
8. A woman goes to market and buys two kinds of drapes. When asked by her husband she says “Don’t worry they together cost less than 10 dollars”. The no. of yards of cloth bought of each type is equal to its cost per yard. Also she spends 2$ and 15 cents more on one type than the other. Find out the no of yards of each cloth.

9. A man starts walking 10 km along X road,turns left and walks 10 km along Y
road ,turns left and walks 10 km along Z road ,turns left and walks 15 km
and turns left and walks 5 km along a road.Which road is he in now?
10. During a party 12 guests were there and each clinked his glasses with the
other.How many clinks were heard totally?

Ans:55

-> 2nd ans is 110 b'coz u 'll get a 11*10 matrix.
-> 4th ans is
a)100km(b'coz they r in a.p)
b)200km
-> 5th ans is 1/3=0.33(this is b'coz two nos can b either > or < or =)
-> 9th X
->10th 11c2=11*10/2=55

1st ans )water : wine = 1:2
===========================
Assume vol wine water
Jar A 100 50 50
Jar B 200 50 150

Jar C 100 200
============================

2nd ans)
i think its 121 .

1--1--1--1--1--1--1--1--1--1--1
|
1
|
1
There are 11 such rows ....

10) formula to find the answer is n-1[SIZE="3"]C[/SIZE]2

here n = 12
so 12-1[SIZE="3"]C[/SIZE]2 = 11[SIZE="3"]C[/SIZE]2= 11 *10 /2 = 55


4) let us assume that they travelled x kms on the first day of the trip.
so on the second day they travelled x +20 kms and x+2*20 kms, x+3*20 kms in third and fourth day respectively.

So the total distance they travelled is
x+ (x+20) + (x+2*20). . .+(x+8*20) = 1080
9x + (1+2+3+...+8)*20 = 1080
9x + (8*9/2) *20 = 1080
9x + 720 = 1080
9x = 1080 -720 = 360
x = 360/9 = 40

a. kms did they travel on the 4th day = 40 + 3*20 = 100 kms
b. kms did they travel on the last day = 40 + 8*20 = 200 kms

5) Porbablility = n(A)/n(S)

n(S) = 1000 x 1000

n(A)
----

if A says 1 then B can say any number between 2 to 1000=> 999 diff ways
if A says 2 then B can say any number between 3 to 1000=> 998 diff ways
if A says 3 then B can say any number between 4 to 1000=> 997 diff ways
. . .
if A says 999 then B can say only 1000=> 1 possible way
if A says 1000 then B can't say any number=> 0 possible ways

so n(A) = 999 + 998 + . . . +1 = 1000 x 999 /2

So probability that B tells a number which is greater than the number told by A= 1000 x 999 / 2 x 1000 x 1000 = 999/2000

Lets assume 12 cuffs and 18 collors (12 + 18 = 30)
A get 6 cuffs and 6 collors (1/2 cuffs and 1/3 collors)
4 cuffs + 2 cuff + 5 collors + 1 collor = 27 cents (let 4 cuffs = 5 collors = r)
r + r / 2 + r + r / 5 = 27 => r = 10
So B get 6 cuffs and 12 collors (1/2 cuffs and 2/3 collors)
4 cuffs + 2 cuffs + 5 collors + 5 collors + 2 collors
r + r / 2 + r + r + 2r / 5 => r = 39
B paid 39 cents.

The answer for the first question that is water : wine is equal to 3:1

couldn under stand last line

1) let total capacity of 1st jar=100l
" " 2nd jar=200l
jar1 wine:water =50:50
jar2 wine:water =50:150
jar3 =jar1 + jar2 => wine:water =100:200 =1:2

2) the situation can be visualized as a 11*11 matrix
we know that the total number of elements in such a matrix =
11*11=121 trees.
3) let x be the number of cuffs given and y be the number of collars.
so eq. 1 => x+y=30 ................(1)
let a be the cost of 1 cuff and b be the cost of 1 collar
money given by A--- ax/2 + by/3 =27
3ax +2by =162
from (1) y=30-x
3ax+2b(30-x)=162........(2)
given 4a=5b
possible solutions are
(2.5,2) or multiples of them
from (2) we see only (2.5,2) satisfies the condition as others give negetive answers.
so cost of 1 cuff 'a' =2.5cents
cost of 1 collar 'b' =2cents
substituting in (2), we get
totla number of cuffs 'x' =12
total number of collars 'y' =18
so Bs things are 6 cuffs and 12 collars and the amount which she owes to the laundry is 6*2.5+12*2=39cents.
4) let the distance travelled on the first day be 'a'k.m
day 2 =a+20*1
day 3 =a+20*2
.
.
.
.
day 9=a+20*8
total distance covered in 9 days =9/2 *(a+(a+20*8))=1080
or a=40 k.m
so distance covered on the 4th day =a+20*3=40+60=100k.m
distance covered on the last day =a+20*8=40+160=200km
5) answer is 1/1000*997/1000 +1/1000*996/1000 ................................................1/1000*1/1000
=1/1000000(997+996+............+1)=.497503
6) on the second day the watch is 10s fast
3rd day 20s fast
so on the 28the day the watch is watch is 270s or 4.5min fast and that night it gains .5 min and overall it becomes 5mins fast in the night of 28th may.

7) A might have got everything correct, i.e 30 correct answers.
this is the only no. which one can be confident upon. if one thinks he got 29 correct answers, he cant say whether he got the other one wrong or he left it, for that matter every other numbers.
so if he gets 30 correct, then this is unique, no other combinations are possible.
9) ithink he's in X road now.X road is actually a twisted road with 5k.m facing down and 5km to the right so totally he walked 5+5=10km along X road though it's not straight.then he reached the junction and turned left to the Y road ,walked straight for 10km.reached another junction and turned left and walked straight along Y road for 10km.reached another junction, turned left and walked straight along Z road for 10km.reached another junction and turned left and walked straight for 15km, now note that after walking 10km thro this road, he'll be retracing his initial path through the X road(X road has a laterally inverted L bend with arms measuring 5km each.

10) i think the answer is 66 =12*11/2.if the person clinging is so friendly that he doesnt hear his cling as he was completely engaged in his activity,then we can subtract 11 from 66 to get 55.

8) let cost per yard of drape 1 =no.of yard =x
let cost per yard of drape 2 =no. of yard =y
total cost for yard 1 =x^2
total cost for yard 2 =Y^2
total cost =X^2 + y^2<10
also given Y^2=x^2+$2.15

solving we get:
first drape 1.98yard
second drape 2.464yard

MY answer is for you to study High School Mathematics.

Giving you the answers for these 10 problems will not give you the skills to solve any other math problem.

#1 Algebra
#2 Draw a picture
#3 Simultaneous Equations
#4 Algebra
#5 Probability
#6 - #12 Algebra