I want to apply for the post in Tata Consultancy Services and for that I want to get the Tata Consultancy Services Aptitude papers of past year so can you provide me that?

As you want to get the Tata Consultancy Services Aptitude papers of past year so here is the information of the same for you:

1) The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?

ans: (1/A) + (1/B) = 1/T
So when you solved, and got 14/45, that was equal to 1/T. To find T, you need to take the reciprocal; T = 45/14,
(3.21)
u
2) If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly?

ans: n(a ^ b) =n(a)+n(b)-n(a v b)
= 0.75+0.55-0.8
= 0.5
(50%)

3) A student's average ( arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the students average score on the 5th test to be 80?

ans: 4 tests sum=78*4=312
5 tests sum=80*5=400
then 5th test score=400-312=88
(88)

4) Rural households have more purchasing power than do urban households at the same income level, since some of the income urban and suburban households use for food and shelter can be used by the rural households for other needs. Which of the following inferences is best supported by the statement made above?
(A) The average rural household includes more people than does the average urban or suburban household.
(B) Rural households have lower food and housing costs than do either urban or suburban households.
(C) Suburban households generally have more purchasing power than do either rural or urban households.
(D) The median income of urban and suburban households is generally higher than that of rural households.
(E) All three types of households spend more of their income on housing than on all other purchases combined.

ans: B

5) Jose is a student of horticulture in the University of Hose. In a horticultural experiment in his final year, 200 seeds were planted in plot I and 300 were planted in plot II. If 57% of the seeds in plot I germinated and 42% of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?

ans: 200 * 57 % = 114 and 300* 42% = 126.
Total = 240 out of 500.
(48%).

6) A closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

ans: What given Volume = 36
Height = 4ft
Volume = Pi* r2 * h
36 = Pi*r2 * 4
r2 =9
r = 3
So the radius is 3 which means the diameter is 6.

7) The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of the teachers would then be 25 to 1 What is the present number of teachers?

ans: 30/1 = s/t Current student to teacher ratio
s+50/t+5 = 25/1 Future student to teacher ratio
solving the first equation first equation for s gives s = 30t.
Substitute this value of s into the second equation, and solve for t.
s+50/t+5 = 25/1
30t + 50 = 25t + 125 multiply both sides by t+5
5t = 75 simplify by subtraction
t = 15
(15)

8) College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from

ans: total=200
neither>=30
chemistry=130
bio=130
maximum common=minimum of the two=130
if neither=30
then common=150+130+30-200=110
range is 110-130

9) Kelly and Chris are moving into a new city. Both of them love books and thus packed several boxes with books. If Chris packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed?

ans: 100-60=40
40:60=2:3

10) A drug that is highly effective in treating many types of infection can, at present, be obtained only from the bark of the ibora, a tree that is quite rare in the wild. It takes the bark of 5,000 trees to make one kilogram of the drug. It follows, therefore, that continued production of the drug must inevitably lead to the ibora's extinction. Which of the following, if true, most seriously weakens the argument above?

ans: The ibora can be propagated from cuttings and grown under cultivation.

11) Machine A produces bolts at a uniform rate of 120 every 40 second, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

ans: Machine A produces 120/40 = 3 bolts in 1 seconds and machine B produces 100/20 = 5 bolts in one second.
Hence, both of them will produce 8 bolts per second.
Hence, they wil take 200/8 = 25 seconds to produce 200 bolts.
(25)

12) Wood smoke contains dangerous toxins that cause changes in human cells. Because wood smoke presents such a high health risk, legislation is needed to regulate the use of open-air fires and wood burning stoves

ans: In valleys where wood is used as the primary heating fuel, the concentration of smoke results in poor air quality.

13) Analysing the good returns that Halocircle Insurance Pvt Ltd was giving, Ratika bought a 1-year, Rs 10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semi-annually.What was the total amount of interest paid on this certificate at maturity?

ans: @8%, for half year you get 400/- 10000x 8/100x1/2=400
for the next year there will be interest on your investment of 10000 and also on your accrue interest of Rs.400/-
that means another 400/+ interest on 400/- @8% for half year.=400+ (400x8/100x1/2)
400+400+16=816

14) Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

ans: 11x/y

15) A certain company retirement plan has a rule of 70 provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?

ans: The female employee must gain at least 70 points.
Now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2 * (number of years) = 70
(Number of years) = 19
So, 1986 + 19 = 2005

16) Homeowners aged 40 to 50 are more likely to purchase ice cream and are more likely to purchase it in larger amounts than are members of any other demographic group. The popular belief that teenagers eat more ice-cream than adults must, therefore, be false. The argument is flawed because the author _____

ans: fails to distinguish between purchasing and consuming

17) Andalusia has been promoting the importance of health maintenance. From January 1,1991 to January 1,1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1,1993 was 45 million. How many million people(to the nearest million) was enrolled in health maintenance organizations on January 1,1991?

ans: let there are 'x' population at jan1,1991
15% of x = 15/100*(x)
(x)+[15/100*(x)]=45 /* as there is 15% increase from 1991 to 1993*/
x=39.13

18) What is the lowest possible integer that is divisible by each of the integers 1 through 7, inclusive?

ans: L.C.M of(1,2,3,4,5,6,7)=2*2*3*5*7=420

19) If the area of a square region having sides of length 6 cms is equal to the area of a rectangular region having width 2.5 cms, then the length of the rectangle, in cms, is

ans: Area of a Square
s x s
6 x 6 = 36
Area of a Rectangle
lw
?(2.5)
=36 as it is equal to the area of a square
36/2.5 = 14.4 cm

20) A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2500 gallons of water evaporate from the tank, the remaining solution will be approximately what percentage of sodium chloride?

ans: Original =10,000 ----> sodium chloride = 5% ie 500
New = 10,000-2,500 = 7500.
New % = (500/7500) * 100
= 6.67%

21) After loading a dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day of the crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?

ans: Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)
Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)
Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes
Combined total boxes for both shifts = 20 + 12 = 32
Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8

22) A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon and 80 % of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?

ans: 4 rolls were not sold.............half of them were sold by noon.......so 20 rolls remain....and then 20% were not sold,, so 20% of the 20 rolls is 4 then it is the answer

23) If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have including n?

ans: 4

24) A dealer originally bought 100 identical batteries at a total cost of q rupees. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many rupees was each battery sold?

ans: bought for q/100 dollars per battery
each battery sold with profit 50% is
q/100 + q/100*50/100
=q/100+q/200
=3q/200

25) The price of lunch for 15 people was 207 pounds, including a 15 percent gratuity of service. What was the average price per person, EXCLUDING the gratuity?

ans: Let the net price excluding the gratuity of service = x pounds
Then, total price including 15% gratuity of service = x + 0.15 x = 1.15 x pounds
So, 1.15 x = 207 pounds
==> x = 207 / 1.15 = 180 pounds
Net price of lunch for each person = 180 / 15 = 12 pounds

26) Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?

ans: For approximation
(50.2*0.49)/199.8 can be taken as
50*0.5/200 = 25/200 = 1/8 = 0.125

27) How many prime numbers between 1 and 100 are factors of 7150?

ans: 7,150 = 2 * 5 * 5 * 11 * 13
so there are 4 distinct prime numbers that are below 100

28) Guitar Strings often go dead - become less responsive and bright in tone - after a few weeks of intense use. A researcher whose son is a classical guitarist hypothesized that dirt and oil, rather than changes in the material properties of the string, were responsible. Which of the following investigations is most likely to yield significant information that would help evaluate the researcher's hypothesis?

ans: Determining whether smearing various substances on new guitar strings causes them to go dead

29) Red blood cells in which the malarial-fever parasite resides are eliminated from a person's body after 120 days. Because the parasite cannot travel to a new generation of red blood cells, any fever that develops in a person more than 120 days after that person has moved to a malaria free region is not due to malarial parasite. Which of the following, if true, most seriously weakens the conclusion above?

ans: In some cases, the parasite that causes malarial fever travels to cells of the spleen, which are less frequently eliminated from a person’s body than are red blood cells.

30) Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks

ans: 7/25

31) When a polygraph test is judged inconclusive, this is no reflection on the examinee. Rather, such a judgment means that the test has failed to show whether the examinee was truthful or untruthful. Nevertheless, employers will sometime refuse to hire a job applicant because of an inconclusive polygraph test result. Which of the following conclusions can most properly be drawn from the information above?

ans: An inconclusive polygraph test result is sometimes unfairly held against the examinee

32) Country Club has an indoor swimming club. Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

ans: Suppose there are x members, non pass members arre 7x/10 which are equal to 12 + 30 = 42
7x/10 = 42
x = 60
There are 60 members in that club

33) A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:

ans: R G W B Y is the bead pattern and it repeats.
Bead want to end with White.
So, the 3rd, 8th, 13th, 18th... beads will be W.
this can be expressed as 5n+3,where n is an integer.(counting no of white bead)
Test each of the answer choices to determine which is multiple of 5 plus a value of 3.Of the options ,only 68=5(13)+3 can be written in the form 5n+3.
So,the answer is 68.

33 A dog taken four leaps for every five leaps of hare but three leaps of the dog is equal to four leaps of the hare. Compare speed?
Let the distance covered by dog in 1 leap is x and hare covered 1 leap is y.
then, 3x = 4y
=> x =(4/3) y
=> 4x =(16/3) y

Then, The ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x : 5y
= (16/3)y : 5y
=(16/3) : 5
= 16:15 Ans...=16:15

34 There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
a)60 b)50 c)80 d)30

the probability of getting a red ball should be maximized so we will keep 1 red ball in the first box and transfer remaining 38 red balls to other box which has green. The reason for doing this only this combination will make the probability of getting red ball is maximum (i.e) 1.
In the question its mentioned that first we have to choose a box at random.
So 2 boxes are there, probability of selecting a bag is 1/2
Probability of getting red ball from first box is 1
Probability of getting green ball from second box is 38/64
So (1/2)*1 for first box and (1/2)*(38/64) for box 2
answer is (1/2)*1 + ((1/2)*(38/64) which is approximately 0.8
Next number in the given series 1, 7, 8, 49, 50, 56, 57, 343
344 because
1*7=7
7+1-8
7*7=49
49+1=50
8*7=56
56+1=57
49*7=343
343+1=344
ans= 344
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?
q.2.in how many ways can 5 postboxes hold 3 post cards?
q.1 in how many ways can 3 postcards can be posted in 5 postboxes?

first post card can be posted in any of the 5 post boxes =5c1 ways
second post card can be posted in any of the 5 post boxes =5c1 ways
third post card can be posted in any of the 5 post boxes =5c1 ways

number of ways=5c1*5c1*5c1=125=5^3

q.2.in how many ways can 5 postboxes hold 3 post cards?
first post box can hold 3 post cards in 3c1 ways
second post box can hold 3 post cards in 3c1 ways
third post box can hold 3 post cards in 3c1 ways
fourth post box can hold 3 post cards in 3c1 ways
fifth post box can hold 3 post cards in 3c1 ways
so number of ways =3c1*3c1*3c1*3c1*3c1=3^5

35 A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have???
Answer for this question is 729
The explanation goes like this
Let a,b,c be three prime no.
since the no. of perfect square as a factor is 125
which can only be if every prime no. has power in the multiple of 2 including zeros(bcoz any no. to the power of zero is a perfect square)
so power must be 0,2,4,6,8
thereby 5*5*5=125
Since no. of cube as a factor is 27
therefore power in the prime no. will be in the multiple of 3
so power are 0,3,6
hence the no. N=a^8*b^8*c^8
hence total no. of factor is (8+1)(8+1)(8+1)=729
there r three buckets..of 8,5 n 3 litres...out of which only 8 ltr bucket is fully filled...u hv to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimm num of steps......
8ltr 5ltr 3ltr
initially 8 0 0
step1 3 5 0
step2 3 2 3
step3 6 2 0
step4 6 0 2
step5 1 5 2
step 6 1 4 3
step 7 4 4 0
total 7 steps

36 The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
a) 41 b) 42 c) 40 d) 43
total=800m
16m per min means for 1m=800/16 =50min to climb
10m per min means for 1m=800/10=80min to climb for paul .....the total time is 2hours==120min....so,time taken for rest by paul is 120-80=40min
length of minute hand is 5.4 cm, area covered by this in 10 min is ?

a)50.97 b)57.23 c)55.45 d)59.14
t will be (3.14*5.4*5.4)*10/60 = 15.26 cm2.

37 Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
a) 1/72 b) 1/9 c) 25/216 d)1/8
ossible event.......(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2, 3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4 ,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5, 1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1 )
total 27 possible event
so probability = 27/216 i.e 1/8
answer-------d(1/8)

Probability of a sum of 3: 1/216 = 0.5%
Probability of a sum of 4: 3/216 = 1.4%
Probability of a sum of 5: 6/216 = 2.8%
Probability of a sum of 6: 10/216 = 4.6%
Probability of a sum of 7: 15/216 = 7.0%
Probability of a sum of 8: 21/216 = 9.7%
Probability of a sum of 9: 25/216 = 11.6%
Probability of a sum of 10: 27/216 = 12.5%
Probability of a sum of 11: 27/216 = 12.5%
Probability of a sum of 12: 25/216 = 11.6%
Probability of a sum of 13: 21/216 = 9.7%
Probability of a sum of 14: 15/216 = 7.0%
Probability of a sum of 15: 10/216 = 4.6%
Probability of a sum of 16: 6/216 = 2.8%
Probability of a sum of 17: 3/216 = 1.4%
Probability of a sum of 18: 1/216 = 0.5%

38 Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is
a) 3.50 b) 10.53 c) 1.17 d)2.8
30L+3Q=11.67
30L+6Q=12.48
------------
3Q=.81 Q= .27
from that L=0.362 cost of 10 kg apple is 10*.362=3.6
The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?
a) ARBSEU
b) ARBESU
c) ARBSUE
d) ARBEUS
AB**** =4!= 24 ways
AE****=4!=24 ways next word is 49th so
AR**** in alphabetical order **** will be BESU
ans is B

39 A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?
ans is 10.5
gn:
A+B=(1/7)
A=2B
=>B=1/21
A=2/21
=>A take (21/2)=10.5 days to complete the work.
In 8*8 chess board what is the total number of squares.
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2=204....
formula=1^2+2^2+3^2+....+n^2

40 X,Y,W,Z ARE INTEGER THE EXPRESSION X-Y-Z IS EVEN&Y-W-Z ODD IF X IS EVEN THEN WHICH OF FOLLOWING IS TRUE(a)Y MUST BE ODD(b)Y-Z MUST BE ODD(c)W MUST BE ODD(d)Z MUST BE ODD
Ans.(c)W must be ODD
X-Y-Z=even and X even no.
hence (y-z) must be even because (even -even = even)
and y-w-z=y-z-w=odd and (y-z) is even so W must be odd because (even - odd=odd)
hence option (c) is correct

41 Two cyclist begin training on oval racecourse at same timethe professional cyclist complete each lap in 4 sec noves take 6 mintue how many mintue after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12
ans is d.
simply LCM of 4 and 6.
which of following true:A occur only B or C occur B occur D&E occurf occur if Cnot occur g occur if A and F occur option A occur whenever F occur2)F never occur3) G not occur if D not occur4)none of these
3) g nt occure i d not occure
a=>b or c
b=>d & e
f=>c not
g =>a & f
1) a occure whenevr f :- depen on c where as 'a' can occure if 'c' not ..so this is not true
2) f nevr occure => depnd on c only n c is indipendent ...if c not occure f will occure ....so this is also not true
3) g not occure if d not:-g depnd on a & f ...if d not ocuure b will not occure (as b=>d&e) a will occure if c occure...if c occure f will not occure ...hence g will not occure...this is true
House1 is older than H2, H3 is taller than H4,H4 is older than H1...(i)H1 is older than H3 (ii)H2 is taller than H4 (a)only 1 (b)both (c)neither (d)only2
c)neither, is the answer.

42 In how many ways can 20 identical pencils be distributed among three girls so that each gets at least 1 pencil? now A'+B'+C''=17,
number of non negative integers of A',B',C' are (17+3-1)C(3-1)
so total Combinations are 19c2=19*9 = 171,
simple formula for this kind of problems is
(n-1)c(r-1)
so 19c2= 171
if p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 & p(0)=48.what is p(5)
if 1 is a root then x-1 is a factor of p(x)
similarly x-2 is a factor,x-3 ,x-4 are factors
but p(x) is 4th degree polynomial therefore it can be in the form
p(x) = Q(x-1)(x-2)(x-3)(x-4) , where Q is a constant
but given p(0) =48
therefore 24 Q =48
Q=2
p(x) =2(x-1)(x-2)(x-3)(x-4)
p(5)= 2*4*3*2*1 = 48
1!+2!+3!...+50! divided by 5!
remainder will be ?
1!+2!+3!...+50! divided by 5!
remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.
so remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120).
so remainder is 33.

43 If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
we have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600

44 An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
a)0.6485
b)0.6565
c)0.8645
d)none of these
ans=c (0.8645)
probablity of nondefective of x= 91/100=.91
probablity of non defective of y= 95/100=.95
so, probablity of nondefective product=.91*.95=0.8645

45 There are six multiple choice questions in the examination. How many sequences of anwers are possible, if the first two question have 3 choices each, the next two have 4 choice each and last two have 5 choices each?
3c1*3c1*4c1*4c1*5c1*5c1=3600
for any one of first three option of Q.1 we have three options in Q.2 4 option in Q.3.....this goes on...
ind the area (in square units) of the triangle formed by 2x+3y=5, y=x and X-Axis.
the points of intersection for lines:
2x+3y=5 and x=y => 5x=5 => x=1 and y=1 =>(1,1)
x=y and y=0(x-axis) => x=0 and y=0 =>(0,0)
2x+3y=5 and y=0(x-axis) => 2x=5 => x=5/2 and y=0 =>(5/2,0)

area of triangle with vertices (x1,y1),(x2,y2),(x3,y3) is
|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|/2
=|1(0-0)+0(0-1)+5/2(1-0)|/2
=|1+5/2|/2
=7/4 sq units...

46 Arun was all bent on building a new house. He carefully got the blue print of his house designed buy his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?
27*48/2*3=216

47 Roy is now 4 year older than Erik and half of that amount than Lewis.If in two years Roy will be twice as old as Erick,then in two year what would be Roy age multiplied by Lewis age??
ans is 48 firstly two equation from 1st sentence ..
suppose roy=x, erik=y, lewis=z
so x=y+4....(1)
2nd is x=z+2...(2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)
also after 2 years erik and roy relation wil b
x+2=2(y+2).. (3)
so put this into 1st equ. u will get y=2..
and then x=6,z=4(by substituting other)
nw asking multiplication after two years of roy n lewis is (6+2)*(4+2)=48..
if there are maximum acute angles then how many convex hectagons are there there can be max 3 acute angles in a convex polygon which is a triangle.

48 The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?
The number of bacteria was growing in a city exponentially.at 4 pm yesterday , the number of bacteria was 400 and at 6 pm yesterday it was 3600.How many bacteria were there at 7pm yesterday?

.49 There are 12 children in a family .the youngest 1 is a boy.then find the probabality of finding boy in the family.
a)4096
b)2048
c)2
d)2!
Probability cannot be more than 1..it ranges from 0 to 1..
there can be two options..either a boy/girl in a family
asked is to find a boy=1/2
given 12 children but it is already mentioned that the youngest is a boy so no need to count that..
hence,1/2*1/2*1/2......(11 times)=1/2048 option b..but the option is wrong..it should be 1/2048

50 A volume of 10936 l is in a conatiner of sphere . how many semispheres of volume 4 l each will be required to transfer all the water into small semispheres?
v10936/4=2734.....is the ans
a volume of A are having in a container of sphere. how many semi hemispheres of B volume each will be required to transfer all the A in to semi hemispheres?
ans is A/B.

51 My name is PREET.But my son accidentally types the by interchanging a pair of letters in my name.What is the probability that despite this interchange, the name remains unchanged? a.5% b.20% c.25% d.12.5%
10%
Selecting any two - 5C2 = 10[ treating E AND E as distinct)
Selecting EE = 1
1/10 * 100 = 10%