Transcript Solution

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
The
fuel
fuel
consumed
consumed
while
going
while
=
coming
X
+
=
¼
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 Numbers
Solution:
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 = 5S
F – 4 = 9(S-4)
F – 5s = 0
F – 9S = -36 + 4 = -32
4S = 32
S=8
Father 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 = -2
P – 2S = 2-1 = 1
S=3
P – 3(3) = -2
P – 9 = -2
P = -2 + 9 = 7
After 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
Alligation or Mixture
•(Quantity of cheaper / Quantity of costlier)
(C.P. of costlier) – (Mean price)
= --------------------------------------
(Mean price) – (C.P. of cheaper)
Alligation or Mixture
Cost of Cheaper
c
Cost of costlier
d
Cost of Mixture
m
d-m
m-c
Alligation or Mixture
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?
Alligation or Mixture
Solution:
7
17
10
(17-10)
(10-7)
7
:
3
The ratio is 7:3
The quantity of 2nd kind = 3/10 of 100kg
= 30kg
Alligation or Mixture
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)
Alligation or Mixture
Answer:
R
:
S
2
:
1
75% :
25%
3
:
1
1 gallon of R should be added.
Alligation or Mixture
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 ?
Alligation or Mixture
Solution:
25
30
x
(30- 28)
(28-25)
2
:
3
Let mixed price be x
If 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
Partnership
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
Share
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
Partnership
Solution
A: B:C
100 : 65 : 35
20 : 13 : 7 Total = 20+13+7 = 40
C’ share = 560
7/40 *X =560
X= 3200
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
Time and Work
• 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
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
Pipes and Cisterns
• 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
Time and Work
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 = 1/30
B + C = 40 days = 1/40
C +A = 60 days = 1/60
All work together
A+B+C+B+C+A = 1/30 +1/40 +1/60
2(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 = 1/15
15 men = 12 days means 1 day work = 1/12
10 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
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.
Time and Work (Pipes)
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.
Time and Work (Pipes)
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
Time and Work (Pipes)
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
Time and Work (Pipes)
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?
Time and Work (Pipes)
Answer :
A = 1/10; B = 1/6
= 1/10 -1/6
= - 1/15
Empty in 15 minutes
To 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.
Area and Volume
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%
Probability
•
Probability:
P(E) = n(E) / n(S)
•
Addition theorem on probability:
n(AUB) = n(A) + n(B) - n(AB)
•
Mutually Exclusive:
P(AUB) = P(A) + P(B)
•
Independent Events:
P(AB) = 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
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?
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)!
Permutations and Combinations
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 …
Permutations and Combinations
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.
Permutations and Combinations
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 ?
Permutations and Combinations
Solution:
It is selection so use combination formula
Programmers and managers = 6C3 * 4C2
= 20 * 6 = 120
Total number of ways = 120 ways.
Permutations and Combinations
In how many ways can the letters of the word
BALLOON be arranged so that two Ls do not
come together?
Permutations and Combinations
Solution:
Total arrangement = 7! / 2!*2! (L and O occurred twice)
=1260
Ls come together (BAOON) (LL)
= 6! / 2!
= 3* 4* 5*6*
= 360
Ls not come together
1260 – 360 = 900
Number of ways = 900.
Permutations and Combinations
A man has 7 friends. In how many ways can
he invite one or more of them to a party?
Permutations and Combinations
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 = 60000
X = 4, 00,000
In 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
Boats and streams
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 =8
Up Stream = Sp. of the boat – Sp. of the stream = 5-3 = 2
Let distance be X
Distance/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
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/hr
48/ (4/x) + 48/(3/x) = 14
x = 1/2
Speed of Downstream = 8,
Speed of upstream
=6
Rate of the stream =1/2 (8-6) km/hr = 1 km/hr
Time and Distance
•Speed:• Distance
covered
per
unit
called speed.
Speed = distance/time (or)
•Distance = speed*time
•Time = distance/speed
(or)
time
is
Time and Distance
• 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
Answer:
Time and Distance
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
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 ?
Time and Distance (Trains)
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.
Time and Distance (Trains)
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
Time and Distance (Trains)
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
Time and Distance (Trains)
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 ?
Time and Distance (Trains)
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
Time and Distance (Trains)
120 m long train crosses the pole after
2½ sec. Find how much time it takes to cross
140 m long platform?
Caritor Question
Time and Distance (Trains)
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.
Time and Distance (Trains)
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?
Time and Distance (Trains)
Solution:
Let the speed of train Y be x km/hr
Relative Speed of X to Y = (120 –x) km/hr
= [(120 –x)*5/18] m/sec
=( 600 – 5x) / 18 m/sec
T = D / Rel. Speed
300 / (600 – 5x /18) = 120 ( 2 Minutes )
5400 = 120 (600 -5x)
x = 111 m/sec.
Odd days:
0 = Sunday
1 = Monday
2 = Tuesday
3 = Wednesday
4 = Thursday
5 = Friday
6 = Saturday
Calendar
Calendar
Month 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
Calendar
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?
Clocks
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
Find the angle between the minute hand and
hour hand of a clock when the time is 7:20.
Clocks
Solution:
 = 30h – (11m/2)
= 30 (7) – 11 20/2
= 210 – 110
= 100
Angle between 7: 20 is 100o
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
Data Interpretation
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.
•
1. The following table gives the distribution of students according to
professional courses:
__________________________________________________________________
Courses
Faculty
___________________________________
Commerce
Boys
Science
girls
Boys
Total
girls
___________________________________________________________
•
Part time management
•
C. A. only
•
Costing only
•
C. A. and Costing
30
150
10
50
10
100
8
16
6
180
90
10
37
3
140
70
2
7
1
80
__________________________________________________________________
•
On the basis of the above table, answer the following questions:
Data Interpretation
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
Answer:
Data Interpretation
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
Answer:
Data Interpretation
Percentage of boys over all students
= (450 x 100) / 500
= 90%
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.