# TCS Aptitude Paper

TCS Aptitude Paper on October is listed in indiahires.in. Get your latest TCS Aptitude Paper from indiahires

Tata Consultancy Services (TCS) is a global leader in IT services, and digital and business solutions that collaborates with customers to simplify, reinforce, and transform their operations. Through a profound dedication to our clients, extensive industry experience, and a global network of innovation and delivery centers, we assure the greatest assurance and satisfaction.

Q1. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled up like 10, 20, 40,80, 160..in tank B. 1/8 th of tank B is filled in 22 hours. What is the time to fill the tank fully?

(a) 26

(b) 25

(c) 5

(d) 27ANS: 25

Explanation:

Tank B is filled in geometric progression, so after 22 hrs water in the tank will be = 10 * 2^21 = x/8

where x = volume of tank x = 10 * 2^24 thus by geometric progression we get that n-1 = 24

so n = 25, hence the time required is  25 hrs.

Q2. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says At least n of the statements on this sheet are false. Which statements are true and which are false?

(a) The even-numbered statements are factual and the odd-numbered are false.

(b) The odd-numbered statements are factual and the even-numbered ones are false.

(c) The first 35 statements are factual and the last 35 are false.

(d) The first 35 statements and the last 35 false statements.ANS: C

Explanation:

Note: For this type of Question, follow this:

–At least- the Ist half is true, Last half is false

–Exactly- Last second one is true or (N-1)the Statement is true

–Almost- All are true.

Aliter :

Suppose the first 35 statements are true!

Statement 1: At least 1 statement is false [TRUE]

Statement 2: At least 2 statements are false   [TRUE]

Statement 35: At least 35 statements are false  [TRUE]

——————————————————————–

Statement 36: At least 36 statements are false  [FALSE]

..

Statement 40: At least 40 statements are false  [FALSE]

——————————————————————-

AT LEAST puts the minimum tag or the floor tag on the statements

So, if the first 35 statements are true and the rest are false, everything fits into place!

Q3. Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red, 10 white, 25 yellow, 55 purple, and 30 orange. The lights are out and it is dark despite the darkness. She can make out the difference between a hat and a glove. She takes an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure she has a pair of each color of blue, red, and yellow?

(a) 59

(b) 8

(c) 50

(d) 42

ANS: a(32+25+2)

Explanation:

Note: For this type of question:

Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1), If you do not find an answer in the options, choose the one closer those the answer you got.

Q4. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of \$7 billion. As one of the forerunners in the technology front, Trump continues to lead the way in products and services in India. At Trump, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate. Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?

For this type of question, you should follow d steps of basic math that will help you get enough time from that.

12 prog 12 line 12 min

1 prog 12 lines 12*12

1 1 12*12/12

72 1 12*12/(12*72)

72 72 12*12*72/(12*72)

ANS: 12

Note: This question appears 3 times in our question but the app is different please follow the basic rules think it is very very easy.

Q5. 12 people {a1, a2, a12} meet and circularly shake hands. In other words, there is a total of 36 handshakes involving the pairs, {a1, a2}, {a2, a3},  {a11, a12}, {a12, a1}. The size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

(a) 12

(b) 4

(c) 18

(d) 11

ANS: A

Explanation:

12 x 11 / 2 = 66 Handshakes

Q6. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities is true?

A. All suspects are lying.

B. leftmost suspect is innocent.

C. leftmost suspect is guilty

(a) A only

(b) A or C

(c) A or B

(d) B only

ANS: C

Explanation:

Here the leftmost person is lying since there is nobody to his right!-U have to visualize the right side of the person and not yours!

Ans is c. Here the leftmost person is lying since there is nobody to his right!-

you have to visualize the right side of the person and not yours!

< 1< 2< 3< 4< 5< 6< 7< 8< 9< 10 this is the right side they are facing u..10th right most of you are not questioned left most of u are 1 he is guilty as he is saying that the person to his right is guilty but there is no one to his right and the first statement is false as 2 is not lying as 1(left most of u) is guilty as 1 is guilty than not innocent so neither of them

Q7. Alok and Bhanu play the following min-max game. Given the expression N = 15 + X*(Y “ Z) Where X, Y, and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single-digit number and Bhanu substitutes this for a variable of her choice (X, Y, or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally, Alok proposes the value for the remaining variable. Assuming both plays to their optimal strategies, the value of N at the end of the game would be?

ANS: 15+18 =33

Q8. How many four-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?

(a) 100

(b) 125

(c) 75

(d) 85

ANS: 5^n-i

Explanation:

1= 5^4-1=125, n= no of digits

—  — 1 2

— — 2 4

— — 3 2

— — 4 4

— — 5 2

The first two digits in the place can be filled in 5 x 5 ways.

So there are totally 25 x 5 = 125 ways

Q9. The age of the two friends was in the ratio of 6:5 if the sum of their ages is 66. Then after how many years their ratio will become 7:6?

a)11

b) 6

c) 10

d) 12

ANS: 6

Explanation:

Let the age of two friends be 6x and 5x

Sum of their ages 66 => 6x + 5x = 66 => 11x = 66 => x=6

The ages will be 36 and 30

(36+k)/(30+k) = 7/6 => 36 x 6 + 6k = 210 + 7k

216 + 6k = 210 + 7k => 6 = k

After 6 years their ages will be in the ratio of 7:6

Q10. The age of the two friends was in the ratio of 2:3 if the sum of their ages is 55. Then after how many years their ratio will become 4:5?

a) 11

b) 33

c) 22

d) 44

ANS: 22

Explanation:

Let the age be the friends be 2x and 3x. Sum of their ages = 55

2x + 3x = 55 => 5x=55 => x=11

Their ages are 22 and 33

After k years both of them will be 22+k and 33+k years old

The ratio of their age at that time will be 4:5

• (22+k)/(33+k)=4/5
• 5(22+k)=4(33+4) => 110 + 5k = 132+4k
• K=132-110 = 22

Q11. A volume of 10936 l water is in a container of spheres. How many semispheres of volume 4l each will be required to transfer all the water into the small semispheres?

a) 2812

b) 8231

c) 2734

d) 4222

ANS: 2734

Q12. A person is manufacturing a house. He bought 20 ropes of wire which has a density of 300 Kg/m3. The height of the building to be constructed is 40 m. If the capacity of the current passed in the wire is 20 A and the voltage capacity is 80 Volts. Then what will be the opposing force to the current if the wire is used?

a) 2
b) 4
c) 8

d) 1600

ANS: 4

Explanation:

by ohms law

v = ir

so r = v/i

so r = 80/20 = 4

Q13. A horse chases a pony 2 hours after the pony runs. The horse takes 3 hours to reach the pony. If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?

a) 46.4
b) 51
c) 53.4

d) 48.6

ANS:48.6

Explanation:

Horse covers = 81*3 = 243 km

So ponys speed = 243/(2+3) = 243/5 = 48.6

Q14. The difference between the two no is 9 and the product of the two is 14. What is the square of their sum?

a)120

b)130

c)137

d)145

Explanation:

One number is x and the other y, then  x – y = 9

(x – y)2 = 81

x2 + y2 = 81 + 2xy = 109

(x+y)2 = x2 + y2 + 2xy = 109 + 28 = 137

Q15) On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called china to start growing on the rocks. Echina grows in the form of a circle, and the relationship between the diameter of this circle and the age of the echidna is given by the formula d = 4*v (t-9) for t = 9 where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echidna at a particular spot as 7mm. How many years back did the solar blast occur?

a) 15
b) 21.25

c) 12.25

d) 14.05

ANS:15

Explanation:

d = 4*(t-9)

Given r = 12 mm

So, d = 24 mm

So,

24 = 4t – 36

4t = 60

t = 15 years

Q16. A man goes 50 km north, then turned left walked 40 km, then turned right? In which direction he is?

a) North

b) South

c) East

d) West

ANS: North

Explanation:

Left and right consecutive movements nullified the change in direction. So, he is in the direction he started with.

Q17. In T. Nagar the building was numbered from 1 to 100. Then how many 6s will be present in the numbers?

a) 18

b) 19

c) 20

d) 21

ANS: 20

Q18. Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success. Rohit once bought a Ferrari. It could go 4 times as fast as Mohan’s old Mercedes. If the speed of Mohan’s Mercedes is 35 km/hr and the distance traveled by the Ferrari is 490 km, find the total time taken for Rohit to drive that distance.

a) 7/2

b) 9/2

c) 238.25

d) 6.18

ANS: 7/2

Explanation:

Mohan speed = 35 Km/hr

Rohit speed = 4 x Mohan speed = 4 x 35 = 140 Kmph

Time taken =Distance / Speed = 490 / 140 = 49/14 = 7/2

Q19. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says  At least n of the statements on this sheet are false. Which statements are true and which are false?

a) The even-numbered statements are factual and the odd-numbered are false.

b) The odd-numbered statements are factual and the even-numbered are false.

c) The first 35 statements are factual and the last 35 are false.

d) The first 35 statements are false and the last 35 are false.

Q20. A man goes north 37km. turns left to go 2km. turns right and goes 17km. turns right and goes 2km. find distance b/w starting ending point.

a) 54

b) 27

c) 81

d) 67

ANS: 54

Explanation:

The distance between the starting and end point is 37 + 17 = 54

Q21. If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mice are required to find the poisoned can?

a) 3

b) 2

c) 6

d) 1

ANS: 5

Explanation:

Have 6 mice for testing,

Give each mouse contents from 5 cans of each

5 5 5 5 5 5

After 14 hours, one of the mice will die

So, we will know which 5 cans must have the poison

Then, take the contents of these 5 cans and give them to the remaining 5 mice each.

We will know in due time which can be poisoned

5C1+5C2+5C3+5C4 = 5 + 10 + 10 + 5 = 30

Q22. If a and b are mixed in a 3:5 ratio and b and c are mixed in an 8:5 ratio if the final mixture is 35 liters, find the amount of b.

a) 13.34

b) 15.73

c) 16.73

d) 9.45

ANS: 15.73

Explanation:

a: b = 3:5

b: c =   8: 5

a:b:c  = 24: 40: 25  and the total is 24+40+25 = 89

(40/89) x 35 = 15.73

Q23. It is the class with a seating arrangement of 4 rows and 8 columns. When the teacher says to start the girl who is sitting in the first row and the first column will say 1, then the next girl sitting behind her will say 4, and the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what u will say?

a) 15

b) 17

c) 14

d) 16ANS: 16

Q24. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?

a) 2

b) 3

c) 48

d) 25ANS: 25

Explanation:

The answer is 25. First, he will select 24 in that the maximum chance is all are red so if we take one more sock, it has to be the other color. Hence, the answer is 24 + 1 = 25

Q25. If Valentine’s Day in 2005 falls on Monday, then on which day will Valentine’s Day fall in 2010?

a) Saturday

b) Thursday

c) Wednesday

d) Sunday: Sunday

Explanation:

FEB. 14, 2005   IS A  MONDAY

From Feb. 14, 2005, to Feb. 14, 2006, there will be 365 days which means one odd day.

So, FEB. 14, 2006   WILL BE A  TUESDAY

From Feb. 14, 2006, to Feb. 14, 2007, there will be 365 days which means one odd day.

So, FEB. 14, 2007   WILL BE A  WEDNESDAY

From Feb. 14, 2007, to Feb. 14, 2008, there will be 365 days which means one odd day.

So, FEB. 14, 2008   WILL BE A  THURSDAY

From Feb. 14, 2008, to Feb. 14, 2009, there will be 366 days

– add one more odd day for Feb.29. Total is 2 strange days.

So FEB. 14, 2009    WILL BE A  SATURDAY

From Feb. 14, 2009, to Feb. 14, 2010, there will be 365 days

one odd day.

So FEB. 14, 2010    WILL BE A  SUNDAY

Q27. An athlete decides to run the same distance in 1/4th less time than she usually took. By how much percent will she have to increase her average speed?

a) 40

b) 44.4

c) 33.3

d) 22.2

ANS: 33.3

Explanation:

(3/4)t=1

t=4/3=1+1/3

She will have to increase her speed by 33.333% to run the same distance 3/4s of the time.

Q28. In a building, there are 5 rooms. Each has an equal area. The length of the room is 4m and the bread ht is 5 m. The height of the rooms is 2m. If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room?

a) 6460

b) 3080

c) 3640

d) 3080

ANS: 6460

Explanation:

Dimensions = 4 x 5 x 2

TSA = 2 (4 x 5 + 5 x 2 + 4 x 2) = 2(20+10+8)=2×38 =  76 sq m

So bricks required = 76 x 17 = 1292

For 5 rooms 1292 x5 = 6460

Q29. One man wants to build a wall. The length and breadth of the wall are 20 and 30 respectively. He needs 35 bricks for one square centimeter then how many bricks does he need?

a) 21,500

b) 30,000

c) 21,000

d) 20,000

ANS: 21000

Explanation:

Area = 20 x 30 = 600 cm^2

Bricks = 600 x 35 = 21000

Q30. In a hotel, we can order two types of varieties, but we can make 6 more varieties at the home. One can choose the four varieties with two from the hotel as a must. Find how many ways one can order.

a) 14

b) 15

c) 56

d) 28

ANS: 15

Explanation:

No of ways of selecting 2 from the hotel (6 choices) = 6C2

And from home (2 choices) = 2C2

2C2 x  6C2  = 1 x 15 = 15 ways

Q31. If a pipe can fill the tank within 6hrs. But due to the leak, it takes 30 min more. Now the tank is full then how much time will it take to empty the tank through the leak.?

a) 78

b) 56

c) 66

d) 59

ANS: 78

Explanation:

Let the capacity of the tank be 6 liters.

The time to fill this tank is 6 hours when there is no leakage.

so in 1 hour, it fills 1 liter.

when leakage is there then it takes 6.5 hours to fill 6 liter

so in 1 hour, it fills 6/6.5 liter.

Time to vacate will be 1-(6/6.5) = 1/13 litre in 1 hour

time to vacate 1 liter will be 13 hours.

For 6 liter it will be 13*6 =78

Q32. The bacteria has the probability of splitting into 3 and the probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with a probability of 1/5. Then which among the following relation is true?

a) P=1/3+1/5*3

b) P=1/5*(1/8-3)

c) p = (1/3) + (3* 1/5)

ANS:c) p = (1/3) + (3* 1/5)

Explanation:

Probability of the bacteria to be dying = 1/3

Hence the probability of survival = 1/5

if they survive, they will be split into 3 more bacteria hence, p = (1/3) + (3* 1/5)

Q33. There is a bacteria that has the probability of dying 1/3 of its total number or it may triple. Find out the probability

A. P=1/3+(2/3*p^3)

B. P=2/3+(2/3*p^3)

C. P=2/3+(1/3*p^3)

D. P=2/3+(2/3*p^3)

ANS: A. P=1/3+(2/3*p^3)

Explanation:

The probability of bacteria dying is 1/3

or it gets tripled, hence the probability of getting tripled is (2/3)*p*p*p that is  (2/3)*p^3

so both the probability combined as P=1/3+(2/3*p^3)

Q34. Amrith told to Anand in front of a Photo that He is the son of my father’s son. Find who is in the picture if amrita has no brothers and sisters.

a) Amrith himself

b) Amriths Uncle

c) Amriths Father

d) Amriths son

ANS: Amriths son

Q35. One person has no siblings and says, the guy in the photo is the only son of my father s son. What is the relation of the guy to the person?

ANS: Son

Q36. One grandfather has 3 grandchildren two of the age difference is 3. The Eldest child’s age is 3 times the youngest child’s age and the eldest child’s age is two years more than the sum of the other two children. Find what is the age of the elder’s child.

a) 8

b) 12

c) 30

d) 10

ANS: 8

Explanation:

Let the age of the eldest child is E, that of an elder child be M and that of the youngest child be Y, then according to the given conditions

E = 3Y  (1) and  E = 2 + M + Y  (2)

The third condition is somewhat complicated, according to this condition two of the age difference is 3 so three cases will arise

1) E – M = 3, ……(3)

2) M – Y = 3, ……(4)

3) E – Y = 3, ……(5)

if we take first of the 3 conditions then on solving (1), (2), and (3) we will get E = 3, M = 0, Y = 1 which is wrong now on solving (1), (2) and (4) we will get E = 15, M = 8, Y = 5

similarly on solving (1), (2), and (5) we will get E = 4.5, M = 1, Y = 1.5

only E = 15, M = 8, and Y = 5 are correct so the age of the elder child is 8 years