blue lotus a ptitude - tcs. problems on numbers a car is filled with 4 ¼ gallons of oil for full...

Blue Lotus

Aptitude - TCS

Problems on Numbers

A car is filled with 4 ¼ gallons of oil for full round trip.

Fuel is taken 1/4 gallon more while going down than

coming up. What is the fuel consumed in coming up?

Problems on Numbers

Let ‘X’ be the quantity of fuel consumed for the trip in one direction

The fuel consumed while going = X + ¼

The fuel consumed while coming = X

Therefore, the fuel consumed for the trip = (X + ¼) + X = 4 ½

2X + ¼ = 4 ½ => 2X = 4 ½ - ¼ => 2X = 4 ¼ => X= 2 gallons approx

Problems on Numbers

A box of 150 packets consists of 1kg packets and 2kg

packets. Total weight of box is 264kg. How many 2kg

packets are there?

Problem on Numbers

114

Problem on Numbers

The cost of 1 pencil, 2 pens and 4 erasers is Rs.

22, while the cost of five pencils, four pens and

two eraser is 32. how much will 3 pencils, 3

pens and 3 eraser? (TCS)

Problem on NumbersSolution:

Let Pencil be x, Pens be y, Erasers be z

x + 2y + 4z = 22

5x + 4y + 2z = 32

Adding we get 6x+6y+6z = 54

3x + 3y + 3z = 27

3 Pencil, 3 Pens and 3 Eraser is Rs. 27.

Problem on Numbers

If the numerator of a fraction is increased by

25% and denominator decrease by 20%, the

new value is 5/4. what is the original value?

(TCS)

Problem on Numbers

Solution:

( x + 25x/100) / (y – 20y/100) = 5/4

125x / 80y = 5/4

x/y = 5/4 * 80/ 125 = 4/5

Puzzle

In 80 coins one coin is counterfiet. What is the

minimum number of weighings to find out

counterfiet coin?

(TCS)

Puzzle

SIX

Puzzle

In a well of 20feet depth, a frog jumps 5feet up in

the morning and comes 4feet down in the

evening,on which day the frog gets out of the

well.

Puzzle

Sixteen

Number System

The number 362 in decimal system is given by

(1362)x in the X system of numbers. find the

value of X.

Number System

In which of the system, decimal number 184 is

equal to 1234?

Number System

5

Number System

Find the value of the 678 to the base 7.

Number System

1656

Number System

The base 5 representation of the decimal number 2048

is _____.

Odd Man Out

a)LINUX b) WINDOWS 98 c)SOLARIS d) SMTP

a)JAVA b) LISP c) Smaltalk d) Eiffle

Odd Man Out

1.HTTP 2.ARP 3.SNMP 4.SAP

1.Linux 2.windows NT 3.sql server 4.Unix

Problems on Ages

Father’s age is 5 times his son's age.4 years back

the father was 9 times older than his son. Find

the father's present age? (TCS)

Problems on Ages

Solution: F = 5SF – 4 = 9(S-4)F – 5s = 0F – 9S = -36 + 4 = -32 4S = 32S = 8Father age = 40 years

Problems on Ages

One year ago Pandit was three times his sister’s

age. Next year he will be only twice her age.

How old will Pandit be after five years?

(TCS)

Problems on Ages

Solution:(P-1) = 3(S -1)P + 1 = 2( s+1)P – 3S = -3 + 2 = -2P – 2S = 2-1 = 1S = 3P – 3(3) = -2P – 9 = -2P = -2 + 9 = 7After 5 years = 12

Problems on Ages

A father is three times as old as his son after 15

years the father will be twice as old as his son’s

age at that time. What is the father’s present

age ? (TCS)

Problems on Ages

Solution:

F = 3S

F + 15 = 2(S +15)

Father’s age = 45, Son’s age = 15

•(Quantity of cheaper / Quantity of costlier)

(C.P. of costlier) – (Mean price)

= --------------------------------------

(Mean price) – (C.P. of cheaper)

Alligation or Mixture


Cost of Cheaper Cost of costlier c d

Cost of Mixture m

d-m m-c

(Cheaper quantity) : (Costlier quantity) = (d – m) : (m – c)

A merchant has 100 kg of salt, part of which he sells at 7% profit and the rest at 17% profit. He gains 10% on the whole. Find the quantity sold at 17% profit?


Solution: 7 17 10 (17-10) (10-7) 7 : 3The ratio is 7:3The quantity of 2nd kind = 3/10 of 100kg = 30kg


A 3-gallon mixture contains one part of S and two

parts of R. In order to change it to mixture containing

25% S how much R should be added?

(TCS)


Answer:

R : S2 : 175% : 25%3 : 1

1 gallon of R should be added.


In two varieties of tea, one costing Rs. 25/kg.

and the other costing RS. 30/kg are blended to

produce blended variety of tea in ratio 2:3. find

the cost price of the mixture ?


Solution: 25 30 x

(30- 28) (28-25) 2 : 3 Let mixed price be xIf you subtract 28 from 30 you will get 2 and if you subtract 25 from 28 you will get 3.


Chain Rule

Direct Proportion :

A B

A B

Indirect Proportion:

A B

A B

Chain Rule

A can copy 50 papers in 10 hours while both A & B can copy 70 papers in 10 hours. Then how many hours are required for B to copy 26 papers?

(TCS)

Chain Rule

A stationary engine has enough fuel to run 12

hours when its tank is 4/5 full. How long will it

run when the tank is 1/3 full?

TCS Question

Chain Rule

Answer:

Tank hours

4/5 12

1/3 x

4/5 x = 12 * 1/3

It will run for 5 hours

Types:

• A invested Rs.x and B invested Rs.y then

A:B = x : y

• A invested Rs. x and after 3 months B invested

Rs. y then the share is

• A:B = x * 12 : y * 9

Partnership

A sum of money is divided among A, B, C such

that for each rupee A gets, B gets 65 paise and c

gets 35 paise if c’s share is Rs. 560. what is the

sum?

TCS

Share

Solution

A : B : C

100 : 65 : 35

20 : 13 : 7 Total = 20+13+7 = 40

C’ share = 560

7/40 *X =560

X= 3200

Partnership

Share

If Rs. 1260 is divided among A, B, C in the

ratio 2 : 3 : 4 what is C’s share?

TCS

Ratio and Proportion

Solution:

C’s Share = 4/9*1260

C’s share = Rs. 560

• If A can do a piece of work in n days,

• then A’s 1 day’s work = 1/n

• If A is thrice as B, then:

Ratio of work done by A and B = 3:1

Time and Work

Pipes and Cisterns

• P1 fills in x hrs. Then part filled in 1 hr is 1/x

• P2 empties in y hrs. Then part emptied in 1 hr

is 1/y

• P1 and P2 both working simultaneously which fills in x

hrs and empties in y hrs resp ( y>x) then net part filled is 1/x – 1/y

• P1 can fill a tank in X hours and P2 can empty the full

tank in y hours( where x>y), then on opening both pipes, the net part empties in hour 1/y -1/x

Pipes and Cisterns

One fast typist types same matter in 2 hours and

another slow typist types the same matter in 3

hours. If both do combine in how much time will

they finish?

TCS Question

Time and Work

Solution:

Fast typist = 1/2 ; slow typist = 1/3 ;

Together:

= 1/2 + 1/3 = 5/6 so 6/5 hrs

The work will be completed in 6/5 Hrs.

Time and Work

A and B can finish a piece of work in 30 days, B and C

in 40 days, while C and A in 60 days .In how many days

A, B and C together can finish the work ?

Time and Work

Solution:A + B = 30 days = 1/30B + C = 40 days = 1/40C +A = 60 days = 1/60All work together A+B+C+B+C+A = 1/30 +1/40 +1/602(A+B+C) = 1/30+1/40+1/60 = (4+3+2) /120 = 9/120*2 = 9/240 = 3/80 = 26 2/3 A, B and C can finish the work in 26 2/3 days

Time and Work

10 men can complete a piece of work in 15 days

and 15 women can complete the same work in 12

days. If all the 10 men and 15 women work

together, In how many days will the work get

completed ?

Time and Work

Solution:10 men = 15 days means 1day work = 1/1515 men = 12 days means 1 day work = 1/1210 men + 15 women = 1/15 + 1/12 = 4+5/60 = 9/60 = 3/20 20/3 days = 6 2/3 days

The work will be completed in 6 2/3 days.

Time and Work

Time and Work

A work done by two people in 24 minutes. One

of them can do this work alone in 40 minutes.

How much time is required to do the same work

by the second person?

TCS Question

Time and Work

Solution :

A and B together = 1/24; A = 1/40; B = ?

= 1/24 – 1/40 = 2/120

= 1/60

The second person will complete in 60 minutes.

A cistern has two taps which fill it in 12 minutes

and 15 minutes respectively. There is also a

waste pipe in the cistern. When all the pipes are

opened, the empty cistern is filled in 20 minutes.

How long will a waste pipe take to empty a full

cistern ?

Time and Work (Pipes)

Solution:This problem is based on 2nd method.All the tap work together = 1/12 + 1/15 - 1/20 = 5/60 + 4/60 – 3/60 = 6/60 = 1/10 The waste pipe can empty the cistern in 10

minutes.


A tap can fill a cistern in 8 hours and another

can empty it in 16 hours. If both the taps are

opened simultaneously, Find the time ( in

hours) to fill the cistern


Solution:

Tap 1 = 1/8 (fill); Tap 2 = 1/16 (empty)

= 1/8 – 1/16

= 1 / 16

Total time taken to fill the cistern = 16 hours



A water tank is 2/5th full. Pipe A can fill the tank

in 10 minutes and the pipe B can empty it in 6

minutes. If both the pipes are open, how long

will it take to empty or fill the tank completely?


Answer :A = 1/10; B = 1/6 = 1/10 -1/6 = - 1/15Empty in 15 minutesTo empty 2/5 of the tank 2/5 * 15 = 6 Time taken (empty)= 6 minutes

Area and Volume

Cube:

• Let each edge of the cube be of length a. then,

• Volume = a3cubic units

• Surface area= 6a2 sq.units.

• Diagonal = √3 a units.

Cylinder:

• Let each of base = r and height ( or length) = h.

• Volume = πr2h

• Surface area = 2 πr h sq. units

• Total Surface Area = 2 πr ( h+ r) units.

Area and Volume

Cone:

• Let radius of base = r and height=h, then

• Slant height, l = √h2 +r2 units

• Volume = 1/3 πr2h cubic units

• Curved surface area = πrl sq.units

• Total surface area = πr (l +r)

Area and Volume

Sphere:

• Let the radius of the sphere be r. then,

• Volume = 4/3 πr3

• Surface area = 4 π r2sq.units

Area and Volume

Circle: A= π r 2

Circumference = 2 π r

Square: A= a 2

Perimeter = 4a

Rectangle: A= l x b

Perimeter= 2( l + b)

Area and Volume

Triangle:

A = ½*base*height

Equilateral = √3/4*(side)2

Area of the Scalene Triangle

S = (a+b+c)/ 2

A = √ s*(s-a) * (s-b)* (s-c)

Area and Volume

One rectangular plate with length 8inches,breadth 11

inches and 2 inches thickness is there. What is the length of

the circular rod with diameter 8 inches and equal to volume

of rectangular plate?

Area and Volume

Area and Volume

If the length of a rectangle is increased by 30% and

the width is decreased by 20%, then the area is

increased by what Percentage?

Area and Volume

4%

Area and Volume

The length of a rectangle is increased by 60%. By

what % would the width have to be decreased to

maintain the same area?

Area and Volume

37.5%

Area and Volume

• Probability:

P(E) = n(E) / n(S)

• Addition theorem on probability:

n(AUB) = n(A) + n(B) - n(AB)

• Mutually Exclusive:

P(AUB) = P(A) + P(B)

• Independent Events:

P(AB) = P(A) * P(B)

Probability

There are 19 red balls and One black ball. Ten balls are placed in one jar and remaining in one jar. What is probability of getting black ball in right jar ?

(Infosys -2008)

Probability

Answer:

Probability is 1/2.

Probability

There are 5 red shoes 4 green shoes. If one

draws randomly a shoe what is the probability of

getting a red shoe?

CTS Question

Probability

Answer:

The probability is 5/9

Probability

A bag contains 2 red, 3 green and 2 blue balls

are to be drawn randomly. Two balls are drawn

at random. What is the probability that the balls

drawn contain only blue balls ?

Probability

Answer :

The probability is 1/21

Probability

Probability

Sam and Jessica are invited to a dance party. If

there are 7 men and 7 women in total at the dance

and 1 woman and 1 man are chosen to lead the

dance, what is the probability that Sam and Jessica

will not chosen to lead the dance ?

Probability

Answer:

The Probability of Selecting = 1/7*7 =

1/49

The Probability of not Selecting = 1-1/49

= 48/49

Probability

The letters of the word SOCIETY are placed

in a row. What is the probability that the three

vowels come together?

Probability

Answer:

Required Probability = (5!*3! )/7!

= 1/7

Average

• Average is a simple way of representing an

entire group in a single value.

• “Average” of a group is defined as:

X = (Sum of items) / (No of items)

Average

Gavaskar’s average in first 50 innings was 50. After the 51st innings his average was 51. How many runs did he make in the 51st innings?

Average

Hansie made the following amounts in seven games of cricket in India: Rs.10, Rs.15, Rs.21, Rs.12, Rs.18, Rs.19 and Rs.17 (all figures in crores).

Find his average earnings.

Average

Average of 5 number is -10 and sum of 3 numbers is 16.

What is the average of other two numbers?

Permutations and Combinations

• Factorial Notation: n! = n(n-1)(n-2)….3.2.1 • Number of Permutations: n!/(n-r)!

• Combinations: n!/r!(n –r)!

A foot race will be held on Saturday. How many

different arrangements of medal winners are

possible if medals will be for first, second and

third place, if there are 10 runners in the race …


Solution:

n = 10

r = 3

n P r = n!/(n-r)!

= 10! / (10-3)!

= 10! / 7!

= 8*9*10

= 720

Number of ways is 720.


To fill a number of vacancies, an Employer must

hire 3 programmers from 6 applicants, and two

managers from 4 applicants. What is total

number of ways in which she can make her

selection ?


Solution:

It is selection so use combination formula

Programmers and managers = 6C3 * 4C2

= 20 * 6 = 120

Total number of ways = 120 ways.


In how many ways can the letters of the word

BALLOON be arranged so that two Ls do not

come together?


Solution:

Total arrangement = 7! / 2!*2! (L and O occurred twice) =1260Ls come together (BAOON) (LL) = 6! / 2! = 3* 4* 5*6* = 360Ls not come together1260 – 360 = 900Number of ways = 900.



A man has 7 friends. In how many ways can

he invite one or more of them to a party?


Solution:

In this problem, the person is going to select his friends for party, he can select one or more person, so

= 7C1 + 7C2+7C3 +7C4 +7C5 +7C6 +7C7

= 127

Number of ways is 127

Percentage

• By a certain Percent, we mean that many

hundredths.

• Thus, x Percent means x hundredths, written

as x%

Percentage

After having spent 35% of the money on

machinery, 40% on raw material, 10% on staff,

a person is left with Rs.60,000. What is the total

amount of money spent on machinery and the

raw materials?

Percentage

Solution:Let total salary =100%Spending:Machinery + Raw material + staff = 35%+40%+10% = 85%Remaining percentage = 100 %– 85% = 15%15 % of X = 60000X = 4, 00,000In this 4, 00,000 75% for machinery and raw material = 4, 00,000* 75/100 = 3, 00,000

Percentage

If the number is 20% more than the other, how much percent is the second number less

than the first?

Percentage

Solution:

Let X =20

= X / (100+X) *100%

= 20 /120 *100%

=16 2/3%

The percentage is 16 2/3%

Percentage

Find the percentage increase in the area of a Rectangle whose length is increased by 20% and breadth is increased by 10%

Percentage

Answer:

Percentage of Area Change=( X +Y+ XY/100)%

=20+10+20*10/100

=32%

Percentage

If A’s income is 40% less than B’s income, then how much percent is B’s income more than A’s income?

Percentage

Answer:

Percentage = R*100%/(100-R) = (40*100)/ (100-40)

=66 2/3%

Percentage

One side of a square is increased by 30%. To maintain the same area by how much percentage the other side will have to be decreased?

Percentage

Answer:

Percentage = r*100%/(100+r)

= (30*100) / 130

= 23 1/3%

Boats and streams

•Up stream – against the stream

•Down stream – along the stream

•u = speed of the boat in still water

•v = speed of stream

•Down stream speed (a)= u+v km / hr

•Up stream speed (b)=u-v km / hr

•u = ½(a+b) km/hr

•V = ½(a-b) km / hr

A man can row Upstream at 12 kmph and

Downstream at 16 kmph. Find the man’s rate in

still water and rate of the current?

Boats and streams

Solution:

Rate in still water = 1/2 (16 + 12) = 14 Kmph

Rate of Current = 1/2 (16 – 12 ) = 2 Kmph

Boats and streams

A Boat is rowed down a river 40 km in 5 hr and

up a river 21 km in 7 hr. Find the speed of the

boat and the river?

Boats and streams

Solution:

Speed of the Boat Downstream = 40/7 = 8 (a)

Speed of the Boat Upstream = 21/7 = 3 (b)

Speed of the Boat = 1/2 ( a + b ) = 1/2 ( 8+3 )

= 5.5 Kmph

Speed of the River = 1/2 ( a – b ) = 1/2 (8 – 3)

= 2.5 kmph

Boats and streams

A boat’s crew rowed down a stream from A to B

and up again in 7 ½ hours. If the stream flows at

3km/hr and speed of boat in still water is 5

km/hr. find the distance from A to B ?

Boats and streams

Solution: Down Stream = Sp. of the boat + Sp. of the stream = 5 +3 =8Up Stream = Sp. of the boat – Sp. of the stream = 5-3 = 2Let distance be XDistance/Speed = Time X/8 + X/2 = 7 ½ X/8 +4X/8 = 15/2 5X / 8 = 15/2 5X = 15/2 * 8 5X = 60 X =12

Boats and streams

Boats and Streams

A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. Find the speed of the boat in still water in km/hr?

Boats and Streams

Solution:

Speed of the boat in upstream = 40/8 = 5 km/hr

Speed of the boat in downstream= 36/6 =6 km/hr

Speed of the boat in still water = (5+6 ) / 2

= 5.5 km/hr

Boats and Streams

A man rows to place 48 km distant and back in 14 hours. He finds that he can row 4 kmph with the stream in the same time as 3 Kmph against the stream. Find the rate of the stream?

Boats and Streams

Solution:Down stream 4 km in x hours. Then,Speed Downstream = 4/x km/hr, Speed Upstream = 3/x km/hr48/ (4/x) + 48/(3/x) = 14x = 1/2Speed of Downstream = 8,Speed of upstream = 6Rate of the stream =1/2 (8-6) km/hr = 1 km/hr

Time and Distance

•Speed:-

• Distance covered per unit time is

called speed.

Speed = distance/time (or)

•Distance = speed*time (or)

•Time = distance/speed

• Distance covered α Time (direct variation).

• Distance covered α speed (direct variation).

• Time α 1/speed (inverse variation).

Time and Distance

• Speed from km/hr to m/sec - (Multi by 5/18).

• Speed from m/sec to km/h, - (Multi by 18/5).

• Average Speed:-

Average speed = Total distance traveled Total time taken

Time and Distance

From height of 8 m a ball fell down and each

time it bounces half the distance back. What

will be the distance traveled?

Sathyam Question

Time and Distance

Solution:

= 8 + 4 + 4+2+2+1+1+0.5+0.5 +….etc.

The total distance traveled is 24 m

Time and Distance

Two cars are 15 km apart. One is running at a

speed of 50 kmph and the other at 40 kmph. How

much time will it take for the two cars to meet?

Sathyam Question

Time and Distance

Solution:

Time taken

=Distance / (S1 – S2)

= 15 / (50 – 40)

= 15 / 10

= 1.5

It will take 1½ hours.

Time and Distance

The center of a storm shifts 22.5 miles in 1 hour. At

the same rate what time will it take to move 60

miles?

TCS Question

Time and Distance

Answer:

For 22.5 miles it takes 1 hour

It means for 60 miles T = D / S

Time taken = 60 / 22.5

It will take 2 2/3 hours.

Time and Distance

Time and Distance

By walking at ¾ of his usual speed, a man

reaches office 20 minutes later than usual.

Find his usual time?

Time and Distance

Solution:

Usual time = Numerator * late time

= 3*20

= 60

Time and Distance

A man on motorcycle rides 110 miles in 330 minutes. What is his average speed in miles per hour?

TCS Question

Time and Distance

Answer:

Speed = D / T =110*60 /330

The average speed = 20 miles/hour

Time and Distance (Trains)

A train starts from Delhi to Madurai and at the

same time another train starts from Madurai to

Delhi after passing each other they complete

their journeys in 9 and 16 hours, respectively.

At what speed does second train travels if first

train travels at 160 km/hr ?


Solution:

Let x be the speed of the second train

S1 / S2 = √T2/T1

160/x = √16/9

160/x = 4/3

x = 120

The speed of second train is 120km/hr.


Two hours after a freight train leaves Delhi a

passenger train leaves the same station traveling in

the same direction at an average speed of 16 km/hr.

After traveling 4 hours the passenger train overtakes

the freight train. What was the average speed of the

freight train? Wipro Question


Solution :

Speed of Passenger train = 16 kmph

Distance = 16*4 = 64

Speed of freight train = Distance / ( S1 + S2 )

= 64 / (4+2)

= 64/6

= 10.6 km/hr

The average speed = 10.6 km/hr


There are 20 poles with a constant distance

between each pole. A train takes 24 sec to

reach the 12 pole. How much time will it take

to reach the last pole ?


Solution:

To cross 11 poles it is taking 24 sec

To cross 19 poles it will take x time

Poles time

11 24

19 x

11x = 19 * 24

x = 19* 24 /11

x = 41.45 sec

It reaches the last pole in 41.45sec


120 m long train crosses the pole after

2½ sec. Find how much time it takes to cross

140 m long platform?

Caritor Question


Solution:

To cross 120 m it is taking 2 ½ sec. (5/2sec)

To cross (120 +140)=260 m it will take x sec

120x = 260*5/2 (apply chain rule)

= 5 5/12

It takes 5 5/12 seconds.


A train X speeding with 120 kmph crossed another train Y, running in the same direction, in 2 minutes. If the lengths of the trains X and Y be 100 m and 200m respectively, what is the speed of train Y?


Solution:Let the speed of train Y be x km/hrRelative Speed of X to Y = (120 –x) km/hr = [(120 –x)*5/18] m/sec =( 600 – 5x) / 18 m/secT = D / Rel. Speed300 / (600 – 5x /18) = 120 ( 2 Minutes ) 5400 = 120 (600 -5x) x = 111 m/sec.

CalendarOdd days:

0 = Sunday

1 = Monday

2 = Tuesday

3 = Wednesday

4 = Thursday

5 = Friday

6 = Saturday

CalendarMonth code: Ordinary year

J = 0 F = 3

M = 3 A = 6

M = 1 J = 4

J = 6 A = 2

S = 5 O = 0

N = 3 D = 5

Month code for leap year after Feb. add 1.

Calendar

Ordinary year = (A + B + C + D )-2

-----------------------take remainder

7

Leap year = (A + B + C + D) – 3

------------------------- take remainder

7

What is the day of the week on 30/09/2007?

Calendar

Solution:

A = 2007 / 7 = 5

B = 2007 / 4 = 501 / 7 = 4

C = 30 / 7 = 2

D = 5

( A + B + C + D )-2

= -----------------------

7

= ( 5 + 4 + 2 + 5) -2

----------------------- = 14/7 = 0 = Sunday

7

Calendar

What was the day of the week on 13th May,

1984?

Calendar

Clock:

•In every Hour, the minute hand gains 55 minutes on the hour hand

•In every hour both the hands coincide once. = (11m/2) – 30h (hour hand to min hand)

= 30h – (11m/2) (min hand to hour hand)

•If you get answer in minus, you have to subtract your

answer with 360 o

Clocks

Clocks

Find the angle between the minute hand and

hour hand of a clock when the time is 7:20.

Solution:

= 30h – (11m/2)

= 30 (7) – 11 20/2

= 210 – 110

= 100

Angle between 7: 20 is 100o

Clocks

Clocks

At what time between 7 and 8 o’clock will the

hands of a clock be in the same straight line but,

not together?

Clocks

Solution: h = 7

= 30h – 11m/2

180 = 30 * 7 – 11 m/2

On simplifying we get ,

5 5/11 min past 7

In interpretation of data, a chart or a graph is

given. Some questions are given below this chart

or graph with some probable answers. The

candidate has to choose the correct answer from

the given probable answers.

Data Interpretation

• 1. The following table gives the distribution of students according to

professional courses:

__________________________________________________________________

Courses Faculty

___________________________________

Commerce Science Total

Boys girls Boys girls

___________________________________________________________

• Part time management 30 10 50 10 100

• C. A. only 150 8 16 6 180

• Costing only 90 10 37 3 140

• C. A. and Costing 70 2 7 1 80

__________________________________________________________________

• On the basis of the above table, answer the following questions:

The percentage of all science students over

Commerce students in all courses is

approximately:

(a) 20.5 (b) 49.4

(c) 61.3 (d) 35.1

Data Interpretation

Answer:

Percentage of science students over commerce

students in all courses = 35.1%

Data Interpretation

What is the average number of girls in all

courses ?

(a) 15 (b) 12.5

(c) 16 (d) 11

Data Interpretation

Answer:

Average number of girls in all courses = 50 / 4

= 12.5

Data Interpretation

What is the percentage of boys in all courses

over the total students?

(a) 90 (b) 80

(c) 70 (d) 76

Data Interpretation

Answer:

Percentage of boys over all students

= (450 x 100) / 500

= 90%

Data Interpretation

Venn Diagram

If X and Y are two sets such that X u Y has 18

elements, X has 8 elements, and Y has 15

elements, how many element does X n Y have?

Venn Diagram

Solution:

We are given n (X uY) = 18, n (X) = 8, n (Y) =15. using the formula.

n( X n Y) = n (X) + n (Y) - n ( X u Y)

n( X n Y) = 8 + 15 – 18

n( X n Y) = 5

Venn Diagram

If S and T are two sets such that S has

21elemnets, T has 32 elements, and S n T has

11 elements, how many element elements does

S u T have?

Venn Diagram

Answer:

n (s) = 21, n (T) = 32, n ( S n T) = 11,

n (S u T) = ?

n (S u T) = n (S) + n( T) – n (S n T)

= 21 + 32 – 11 = 42

Venn Diagram

If A and B are two sets such that A has 40

elements, A u B has 60 elements and A n B

has 10 elements, how many element elements

does B have?

Venn Diagram

Answer:

n ( A) = 40, n ( n B) = 60 and n ( A n B) = 10,

n ( A u B) = n ( A) + n (B) – n ( A n B)

60 = 40 + n (B) – 10

n (B) = 30

Venn Diagram

In a group of 1000 people, there are 750 people

who can speak Hindi and 400 who can speak

English. How many can Speak Hindi only?

Answer:

n( H u E) = 1000, n (H) = 750, n (E) = 400,

n( H u E) = n (H) + n (E) – n( H n E)

1000 = 750 +400 – n ( H n E)

n ( H n E) = 1150 – 100 = 150

No. of people can speak Hindi only

_

= n ( H n E) = n ( H) – n( H n E)

= 750 – 150 = 600

Venn Diagram

In a class of 100 students, the number of students passed in English only is 46, in maths only is 46, in commerce only is 58. the number who passes in English and Maths is 16, Maths and commerce is 24 and English and commerce is 26, and the number who passed in all the subject is 7. find the number of the students who failed in all the subjects.

Venn Diagram

Solution:

No. of students who passed in one or more subjects

= 11+ 9 + 13 + 17 + 15 + 19 + 7 = 91

No of students who failed in all the subjects

= 100 -91 = 9

Venn Diagram

In a group of 15, 7 have studied Latin, 8 have

studied Greek, and 3 have not studied either.

How many of these studied both Latin and

Greek?

Venn Diagram

Answer:

3 of them studied both Latin and Greek.

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