Transcript Solution

Blue Lotus
Aptitude
Numerical Reasoning
Numerical Reasoning
• Problems on Numbers
• Problems on Ages
• Ratio and Proportion
• Alligation or Mixture
• Chain Rule
• Partnership
• Venn Diagram
Numerical Reasoning
• Area and Volume
• Probability
• Time and Work (Pipes)
• SI and CI
• Average
• Permutation and Combination
• Percentage
Numerical Reasoning
• Boats and Streams
• Time and Distance (Trains)
• Data Sufficiency
• Profit and Loss
• Calendar
• Clocks
• Data Interpretation
• Cubes
Problems on Numbers
Division Algorithm:
Dividend = the number to be divided.
Divisor = the number by which it is divided.
Dividend / Divisor = Quotient.
Quotient * Divisor = Dividend.
Quotient * Divisor + Remainder = Dividend.
Problems on Numbers
Arithmetic Progression:
The nth term of A.P. is given by
Tn = a + (n – 1)d;
Sum of n terms of A.P
Sn = n/2 *(a + L)
or
n/2 *[2a+(n-1)d)]
a = 1st term, n = number of term, d= difference, Tn = nth term
Geometrical Progression:
Tn = arn – 1.
Sn = a(rn – 1)/(r-1);
Where a = 1st term ,
r = 1st term / 2nd term
Basic Formulae
1. ( a+b)2 = a2 + b2 + 2ab
2. (a-b)2 = a2 +b2 -2ab
3. ( a+b)2 - (a – b)2 = 4ab
4. (a+b)2 + (a – b)2 = 2 (a2 +b2)
5. (a2 – b2) = (a+b) (a-b)
6. (a+b+c)2 =a2 +b2 +c2 + 2(ab +bc+ca)
7. (a3 +b3) = ( a+b) (a2 +ab +b2)
8. (a3 –b3) = (a-b) (a2 - ab + b2)
Problems on Numbers
Three numbers are in the ratio 3:4:5. the sum of
the largest and the smallest equal to the sum of
the third and 52. Find the smallest number ?
Problems on Numbers
Solution:
Let the numbers be 3x, 4x and 5x
Then 5x+3x = 4x +52
8x – 4x = 52
4x = 52
x = 52/4
x = 13
The smallest number = 3x = 3*13 = 39.
Problems on Numbers
What is one half of two third of three fourths of
four fifths of five sixth of six sevenths of seven
eights of eight ninth of nine tenths of thirty?
Problems on Numbers
Solution:
= ½ * 2/3 *3/4 * 4/5 * 5/6*6/7*7/8*8/9*9/10 *30
=3
Problem on Numbers
If the operation ^ is defined by the
equator x ^ y = 2x + y what is the value
of a in 2 ^ a = a ^ 3?
(Sathyam)
Problem on Numbers
Solution:
2(2) = a ^ 3
4 + a = 2a + 3
a=1
Problem on Numbers
There are 150 weight some are 1 kg weight and
some are 2 kg weights. The sum of the weights
is 260. what is the number of 1 kg weight.
(TCS)
Problem on Numbers
Solution:
X + 2Y = 260
X + Y = 150
On Solving Two Equations Y = 110
X + Y = 150
X = 150 – 110 = 40 Kg
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
Problem on Numbers
The difference between two numbers is 1/7 of
the sum of these two numbers. What is the
ratio of the two numbers?
(Wipro)
Problem on Numbers
(x- y ) = 1/7 (x+y)
7( x- y) =( x + y)
7x – 7y = x + y
6x = 8y
x/y = 3 / 4
Problem on Numbers
A fraction has a denominator greater than its
numerator by 4. but if you add 10 to the denominator,
the value of the fraction would then become 1/8, what
is the fraction? (Caritor)
Problem on Numbers
Solution:
x/(x+4+10) = 1/8
x/(x+14) = 1/8
8x =( x + 14)
7x = 14; hence
x=2
x/(x+4 )= 2/(2+4 )= 2/6
Problems on Ages
The ages of two persons differ by 10 years. If 5
years ago, the elder one be 2 times as old as the
younger one, find their present ages.
Problems on Ages
Solution:
x - y = 10; x = 10 + y
x - 5 = 2(y-5)
y + 10 -5 = 2y -10
y+5 = 2y -10
2y- y = 15
y=15 and x = 25
Their present ages are 15 years and 25 years.
Problems on Ages
The present ages of three persons are in the
proportion of 4:7:9. Eight years ago, the sum
of their ages was 56. Find their present ages ?
Problems on Ages
Solution:
Three person’s ratio = 4:7:9 Total = 4+7+9 = 20
Sum of their age = 56,
after 8 years their sum = 56 +24 = 80
A’s age = 4/20 *80 = 16
B’s age = 7/20 *80 = 28
C’s age = 9/20 *80 = 36
Their present ages are 16, 28 and 36.
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 30 years older than his son, however
he will be only thrice as old as his son after 5
years what is father’s present age?
Problems on Ages
Solution:
F = S + 30
F + 5 = 3(S+5)
S+30 + 5 = 3S + 15
2S = 20
S= 10
F = 10 + 30 = 40
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
Ratio and Proportion
•
Ratio: The Relationship between two
variables is ratio.
•
Proportion: The relationship between
two ratios is proportion.
Ratio and Proportion
The two ratios are a : b and the sum nos. is x
ax
bx
-------- and ------a+b
a+b
Similarly for 3 numbers a : b : c
Ratio and Proportion
If Rs. 1260 is divided among A, B, C in the
ratio 2 : 3 : 4 what is C’s share?
Ratio and Proportion
Solution:
C’s Share = 4/9*1260
C’s share = Rs. 560
Ratio and Proportion
To 15 liters of water containing 20% alcohol,
we add 5 liters of pure water. What is the % of
alcohol?
Ratio and Proportion
Solution:
15 lit
20 lit (15+5)
= 15%
15% alcohol
20 %
x
by solving we get
Ratio and Proportion
What number should be added or subtracted
from each term of the ratio 17 : 24 so that it
becomes equal to 1 : 2
Ratio and Proportion
Solution:
Let the number be x.
17 + x/24 + x = 1/2
Solving the above equation,
The number to be subtracted is 10.
Ratio and Proportion
The ratio of white balls and black balls is 1:2. If
9 gray balls are added it becomes 2:4:3. Then
what is the number of black balls ?
Ratio and Proportion
Solution:
Ratio of all the three balls = 2:4:3
Ratio of two balls before adding gray = 1:2
9 gray ratio =3
3 parts = 9 balls
1 part = 9/3
4 parts =?
= 9*4/3 =12
Number of black balls is 12
Ratio and Proportion
Rs. 770 was divided among A, B and C such that
A receives 2/ 9th of what B and C together
receive. Find A’s share?
Ratio and Proportion
Solution:
A = 2/9 (B+C)
B+C =9A/2
A+B+C = 770
A + 9A/2 = 770
11A = 770*2
A = 140
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?
Alligation or Mixture
Answer:
R
:
S
2
:
1
75% :
25%
3
:
1
1 gallon of R should be added.
Alligation or Mixture
In an examination out of 480 students 85% of
the girls and 70% of the boys passed. How
many boys appeared in the examination if total
pass percentage was 75%
Alligation or Mixture
Solution:
70
85
75
10
5
Number of Boys = 480 * 10/15
Number of Boys = 320
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.
Alligation or Mixture
A person has Rs. 5000. He invests a part of it
at 3% per annum and the remainder at 8% per
annum simple interest. His total income in 3
years is Rs. 750. Find the sum invested at
different rates of interest.
Alligation or Mixture
Solution:
Average rate of interest = 5% per annum
3%
8%
5%
3%
2%
Investment at 3% per annum = 3x5000/5= 3000
Investment at 8% per annum = 2x5000/5=2000
Chain Rule
Direct Proportion :
A
B
A
B
Indirect Proportion:
A
B
A
B
Chain Rule
• A Garrison of 500 men had provision for 27
days. After 3 days, a reinforcement of 300 men
arrived. The remaining food will now last for
how many days?
Chain Rule
Solution:
Men
days
500
24
800
x
800X = 500x24
X =(500x24)/800 =15 days
Chain Rule
If 20 men take 15 days to complete a job. In how
many days will 25 men finish the work?
CTS Question
Chain Rule
Solution:
Men
Days
20
15
25
x
x/15=20/25
x = (20*15)/25 =12
They will take 12 days
Chain Rule
If 11.25m of a uniform iron rod weighs 42.75 kg,
what will be weight of 6m of the same rod?
Chain Rule
Solution:
length ( m )
11.25
weight ( kg )
42.75
6
x
Since it is a direct proportion,
x
6
6 x 42.75
--------- = --------  x = --------------42.75
11.25
11.25
The weight of rods x = 22.8 kg
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
Chain Rule
20 men complete one - third of a piece of work
in 20 days. How many more men should be
employed to finish the rest of the work in 25
more days?
Chain Rule
Solution:
Men days work
20
20
1/3
work done = 1/3
x
25
2/3
remaining = 1-1/3=2/3
More work, more men (direct proportion)
More days, less men (indirect Proportion)
1/3 *X = (2/3 )*20*(20 /25)
X = 800/25 = 32
More men to be employed = (32-20)
12 More people needed to finish the job
Chain Rule
15 men take 21 days of 8 hrs each to do a piece
of work. How many days of 6 hrs each would
21 women take, if 3 women do as much work
as two men?
Chain Rule
Solution:
3 women = 2 men
21 women = 14 men
Men
Days
Hrs
15
21
8
14
x
6
x/21=(15/14)/(8/6)
x= 30 days
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
Partnership
Sanjiv started a business by investing Rs. 36000.
After 3 months Rajiv joined him by investing Rs.
36000. Out of an annual profit of Rs. 37100 find
the share of each.
Satyam Question
Partnership
Solution :
36000 * 12
: 36000 * 9
4
:
3
Sanjiv’s share of profit = (4*37100)/7 = 21200
profit = 21200
Rajiv’s share of profit = 15900
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?
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
Partnership
A starts business with Rs.3500 and 5 months
after B joins A as his partner. After a year the
profits are divided in the ratio of 2:3. How much
did B contribute ?
Partnership
Solution:
A :B =3500*12 : 7X
42000 : 7X = 2: 3
7X * 2 = 42000 *3
X = 42000 * 3/14
X = 9000
B’s contribution is Rs.9000
Partnership
A and B invest in a business in the ratio 3 : 2. If
5% of the total profit goes to charity and A’s
share is Rs. 855 what is the total profit?
Partnership
Solution:
A : B = 3:2
Let Profit be X
X – 5% of X
X- 5X/100 = 95X/100
3/5 * 95X/100 = 285
19X= 28500
X = 26500/19 = 1500
Total profit is Rs.1500
Partnership
A and B enter into partnership for a year. A
contributes Rs.1500 and B Rs. 2000. After 4
months, they admit C who contributes Rs. 2250.
If B withdraws his contribution after 9 months,
find their profit share ratio at the end of the year?
Partnership
Solution:
A: B: C = 1500*12: 2000*9: 2250*8
= 18000: 18000: 18000
= 1: 1: 1
Profit share at the end of the year,
1: 1: 1
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
What is the cost of planting the field in the form
of the triangle whose base is 2.8 m and height
3.2 m at the rate of Rs.100 / m2
Area and Volume
Solution:
Area of triangular field = 1/2 * 3.2 * 2.8 m2
= 4.48 m2
Cost = Rs.100 * 4.48
= Rs.448.
Area and Volume
Area of a rhombus is 850 cm2. If one of its
diagonal is 34 cm. Find the length of the other
diagonal?
Area and Volume
Solution:
850 = ½ * d1 * d2
= ½ * 34 * d2
= 17 d2
d2 = 850 / 17
= 50 cm
Second diagonal = 50cm
Area and Volume
A grocer is storing small cereal boxes in
large cartons that measure 25 inches by 42 inches
by 60 inches. If the measurement of each small
cereal box is 7 inches by 6 inches by 5 inches then
what is maximum number of small cereal boxes
that can be placed in each large carton ?
Area and Volume
Solution:
No. of small boxes = (25*42*60 ) / ( 7*6*5 )
= 300
300 boxes of cereal box can be placed.
Area and Volume
If the radius of a circle is diminished by 10%,
what is the change in the area in percentage?
Area and Volume
Solution:
= D1 + D2 – D1*D2 /100
= 10 + 10 – 10*10/100
= 20 -1
= 19%
New area changed = 19%.
Area and Volume
A circular wire of radius 42 cm is bent in the
form of a rectangle whose sides are in the ratio
of 6:5. Find the smaller side of the rectangle?
Area and Volume
Solution:
length of wire = 2 πr = (22/7*14*14)cm
= 264cm
Perimeter of Rectangle = 2(6x+5x) cm
= 22xcm
22x =264
x = 12 cm
Smaller side = (5*12) cm = 60 cm
Area and Volume
A man is running around a rectangle. It takes
time, 2 times in traveling length than traveling
width and the total perimeter is 300 m. Find the
Area?.
Area and Volume
Solution:
Breadth = X
Length = 2X
Area = 2X*X = 2X2
Perimeter
6X = 300m
X = 50m
Area = 2x2 =2*50*50
Area = 5000 sq.m.
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
Simple / Compound Interest
Simple Interest = PNR / 100
Amount A = P + PNR / 100
When Interest is Compound annually:
Amount = P (1 + R / 100)n
Compound Interest = A - P
Simple / Compound Interest
•
Half-yearly C.I.:
Amount = P (1+(R/2)/100)2n
•
Quarterly C.I. :
Amount = P (1+(R/4)/100)4n
Simple/compound interest
Difference between C.I and S.I for 2 years
= P*(R/100)2.
Difference between C.I and S.I for 3 years
= P{(R/100)3+3 (R/100)2 }
Simple / Compound Interest
What is the S.I. on Rs. 3000 at 18% per
annum for the period from 4th Feb 1995 to
18th April 1995
Sathyam Question
Simple / Compound Interest
Answer:
Time = 24+ 31+17 = 73 days = 73/365 = 1/5
P = 3000; R = 18%;
= PNR/100 = 3000*1*18/100*5
The simple interest is Rs. 108
Simple / Compound Interest
A sum of money doubles itself at C.I. in 15
years. In how many years will it become eight
times?
Satyam Question
Simple / Compound Interest
Solution:
A = P(1+R/100)15
2P =P(1+R/100) 15 ;
2 = (1+R/100)15
If A = 8P
8P = P(1+R/100)n
23 = ( 1+R/100)
[(1+R/100) 15]3 = (1+R/100)n
n = 3*15
It will take a period of 45 years.
Simple / Compound Interest
Raja borrowed a certain money at a certain
rate of S.I. After 5 years, he had to pay back
twice the amount that he had borrowed. What
was the rate of interest?
TCS Question
Simple / Compound Interest
Solution:
A = 2P
A = P + PNR/100
2P = P(1+NR/100)
2 = (1+5*R/100)
1 = R/20
The rate of interest is 20%
Simple/compound interest
In simple interest what sum amounts to Rs. 1120
in 4 years and Rs. 1200 in 5 years?
CTS Question
Simple/Compound interest
Answer :
Interest for 1 year = 1200 – 1120 = 80
Interest for 4 year = 80*4 = 320
A = 1120
P = A – P = 1120 – 320
The Principal is Rs. 800
Simple/Compound interest
A simple interest amount for Rs. 5000 for 6
months is Rs. 200. What is the annual rate of
interest?
CTS Question
Simple/Compound interest
Solution:
P = 5000; N = 6/12 = ½
I = 200
R = I *100 / P*N
=200*100*2/5000*1
= 40/5 = 8%
The annual rate of interest is 8%
Simple/Compound interest
A man earns Rs. 450 as an interest in 2 years on
a certain sum invested with a company at the rate
of 12% per annum. Find the sum invested.
Simple/Compound interest
Solution:
P = I*100/R*N
= 450*100/12*2
Principal = Rs. 1875
Simple/Compound interest
If Rs. 85 amounts to Rs. 95 in 3 years, what
Rs. 102 will amount in 5 years at the same rate
percent?
Simple/Compound interest
Solution:
Let P = Rs. 85; A = Rs. 95; I = 10/3 in 1 year
Rate = I*100/P*N =4% ( app)
Amount = P+PNR/100 = 102+20 =122
Hence the amount in 5 years = Rs. 122
Simple/Compound interest
What will be the difference between S.I and C.I
on a sum of Rs. 4500 put for 2 years at 5% per
annum?
Simple/Compound interest
Solution:
C.I – S.I = P (R/100)2
= 4500(5/100)2 = 11.25
Difference = Rs. 11.25
Simple/Compound interest
What will be the C.I on Rs. 15625 for 2½ years
at 4% per annum?
Simple/Compound interest
Solution:
A = P(1+R/100)n
A = 15625 [(1+4/100)2 ( 1+(4*1/2) / 100)]
= 17238
C.I = A – P
C.I = 17238 - 15625
Compound interest = Rs. 1613
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
Total temperature for the month of September
is 840C. If the average temperature of that
month is 28C. Find out the days in the month
of September?
Average
Solution
Number of days= 840/28=30 days
Average
The painter is paid x rupees for painting
every 10m of a wall and y rupees for painting
every extra meter. During one week, he
painted 10m on Monday, 13m on Tuesday,
12m on Wednesday, 11m on Thursday and
12m on Friday. What is his average daily
earning in rupees for the five day week?
Average
Solution:
Day 1 = x, Day 2 = x+3y, Day 3 = x+2y,
Day 4 = x+y, Day 5 = x+2y
Average = (x+ x+3y+ x+2y+ x+y+ x+2y) / 5
= 5x+8y / 5 = 5x/5 + 8y / 5
Average for 5 days is x+ (8y/5)
Average
The average of 11 observations is 60. If the
average of 1st five observations is 58 and that
of last five is 56, find sixth observation?
Average
Solution:
5 observations average = 58
Sum = 58*5 = 290
Last 5 observation average = 56
Sum = 56*5 = 280
Total sum of 10 numbers = 570
Total sum of 11 numbers = 660
6th number = 90
(290 + 280)
(11*60)
(660 -570)
Average
The average of age of 30 students is 9 years. If
the age of their teacher included, it becomes 10
years. Find the age of the teacher?
Average
Solution:
Total age of 30 students
= 30*9 = 270
Including the teacher’s age = 31*10 = 310
Difference is = 310-270 = 40 years
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
Two numbers are respectively 30% and 40%
less than a third number. What is the second
number as a percentage of first?
Percentage
Solution:
Let 3rd number be x.
1st number = x – 30% of x = x – 30x/100 = 70x/ 100 = 7x/10
2nd number = x – 40% of x = x – 40x/100 = 60x/ 100 = 6x/10
Suppose 2nd number = y% of 1st number
6x / 10 = (y/100 )* 7x /10
y = 600 / 7
y = 85 5/7
Hence it is 85 5/7%
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
An empty fuel tank of a car was filled with A
type petrol. When the tank was half empty, it
was filled with B type petrol. Again when the
tank was half empty, it was filled with A type
petrol. When the tank was half – empty again,
it was filled with B type petrol. What is the
percentage of A type petrol at present in the
tank?
Percentage
Solution:
Let capacity of the tank be 100 liters. Then,
Initially: A type petrol = 100 liters
After 1st operation:
A = 100/2 = 50 liters, B = 50 liters
After 2nd operation:
A = 50 / 2+50 = 75 liters, B = 50/2 = 25 liters
After 3rd operation:
A = 75/2= 37.5 liters, B = 25/2 +50 = 62.5 liters
Required Percentage of Type A is = 37.5%
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.
Profit and Loss
• Cost Price.
- CP
• Selling Price. - SP
• Profit or Gain. - P = SP – CP
• Loss.
- L = CP - SP
Profit and Loss
.
• Gain% = [(Gain*100)/C.P.]
• Loss% = [(Loss*100)/C.P.]
• S.P. = ((100 + Gain%)/100)C.P.
• S.P. = ((100 – Loss%)/100)C.P.
Profit and Loss
Anu bought a necklace for Rs. 750 and sold it for
Rs. 675. Find her Loss percentage?.
Profit and Loss
Solution:
CP = 750,
SP = 675
Loss% = loss /CP *100
= 75*100/750
= 10%
Loss 10%
L = 750 – 675 = 75
Profit and Loss
A shopkeeper bought a watch for Rs. 400 and
sold it for Rs. 500. What is his profit percentage?
TCS Question
Profit and Loss
Solution:
CP = 400;
SP = 500
Profit % = Profit /CP *100
= 100*100/400
= 25%
Profit 25%
P = 500 – 400 = 100
Profit and Loss
By Selling 15 Mangoes , a Fruit vendor recovers
the cost price of 20 Mangoes. Find the profit
percentage?
Profit and Loss
Solution:
The expenditure and the revenue are equated,
Percentage of profit =Goods left*100
Goods sold
= ( 5*100 ) /15 = 33.3%
Profit and Loss
A shopkeeper loses 7% by selling a cricket ball
for Rs. 31. for how much should he sell the ball
so as to gain 5%
Profit and Loss
Solution:
First case S.P = Rs. 31 and Loss% = 7%
C.P = [100/(100 – loss%)]*S.P = (100*31) / (100-7)
= 100 / 3
Second case, C.P = Rs 100 / 3 and gain% = 5%
S.P = [(100+gain 5%) / 100]*C.P
= [ (100+5 ) / 100] * 100/3
= Rs. 35
Profit and Loss
What is the selling price of a Toy car if the cost
of the car is Rs. 60 and a profit of 10% over
selling price is earned?
CTS Question
Profit and Loss
Solution:
Profit = 60*10/100
=6
Selling Price = C.P + Profit
= 60 + 6
Selling Price = Rs. 66
Profit and Loss
Find the single discount to a series discount
20%, 10% and 5%.
Profit and Loss
Answer:
SP = [( 80*90*95 )/ 100*100*100 ]* CP
= 0.684 CP
Discount = (1 – 0.684) * 100%
= 0.316 *100 %
Discount = 31.6%
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?
Calendar
Solution:
A = 1984 / 7 = 3
B = 1984 / 4 = 496 / 7 = 6
C = 13 / 7 = 6
D=2
( A + B + C + D) -3
= ----------------------7
= 14/7= 0, Sunday.
Calendar
On what dates of April 2005 did Sunday fall?
Calendar
Solution:
You should find for 1st April 2005 and then you find the Sundays
date.
A = 2005 / 7 = 3
B = 2005 / 4 = 501 / 7
=4
C=1/7=1
D=6
(A + B + C + D) -2
= ----------------------7
3 + 4 + 1 + 6 -2
----------------------- = 12 / 7 = 5 = Friday.
7
1st is Friday means Sunday falls on 3, 10, 17, 24
Calendar
What was the day on 5th January 1986?
Calendar
Solution:
A = 1986 / 7 = 5
B = 1986 / 4 = 496/7 = 6
C=5/7=5
D=0
(A + B + C + D) -2
= ----------------------7
5 + 6 + 5 + 0-2
= ----------------------- = 14 / 7 = Sunday
7
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
How many times in a day, the hands of a
clock are straight?
Clocks
Solution:
In 12 hours, the hands coincide or are in
opposite direction 22 times a day.
In 24 hours, the hands coincide or are in
opposite direction 44 times a day.
Clocks
How many times do the hands of a clock
coincide in a day?
Clocks
Solution:
In 12 hours, the hands coincide or are in
opposite direction 11 times a day.
In 24 hours, the hands coincide or are in
opposite direction 22 times a day.
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
Clocks
At what time between 5 and 6 o’clock will the
hands of a clock be at right angles?
Clocks
Solution:
h=5
90 = 30 * 5 – 11m/2
Solving
10 10/11 minutes past 5
Clocks
Find the angle between the two hands of a clock
at 15 minutes past 4 o’clock
Clocks
Solution:
Angle
 = 30h – 11m/2
= 30*4 – 11*15 / 2
The angle is 37.5o
Clocks
At what time between 5 and 6 o’clock are the
hands of a clock together?
Clocks
Solution: h = 5
O = 30 * 5 – 11m/2
m = 27 3/11
Solving
27 3/11 minutes past 5
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%
Data Sufficiency
Find given data is sufficient to solve
problem or not.
A.If statement I alone is sufficient
statement II alone is not sufficient
B.If statement II alone is sufficient
statement I alone is not sufficient
C.If both statements together are sufficient
neither of statement alone is sufficient.
D.If both together are not sufficient
the
but
but
but
Data Sufficiency
What is John’s age?
I. In 15 years will be twice as old as Dias
would be
II. Dias was born 5 years ago.
(Wipro)
Data Sufficiency
Answer:
c) If both statements together are sufficient but
neither of statement alone is sufficient.
Data Sufficiency
What is the distance from city A to city C in
kms?
I. City A is 90 kms from city B.
II.City B is 30 kms from city C
Data Sufficiency
Answer:
d) If both together are not sufficient
Data Sufficiency
If A, B, C are real numbers, Is A = C?
I. A – B = B – C
II. A – 2C = C – 2B
Data Sufficiency
Answer:
D . If both together are not sufficient
Data Sufficiency
What is the 30th term of a given sequence?
I. The first two term of the sequence are 1, ½
II. The common difference is -1/2
Data Sufficiency
Answer:
A. If statement I alone is sufficient but
statement II alone is not sufficient
Data Sufficiency
Was Avinash early, on time or late for work?
I. He thought his watch was 10 minute fast.
II. Actually his watch was 5 minutes slow.
Data Sufficiency
Answer:
D. If both together are not sufficient
Data Sufficiency
What is the value of A if A is an integer?
I. A4 = 1
II. A3 + 1 = 0
Data Sufficiency
Answer:
B. If statement II alone is sufficient but
statement I alone is not sufficient
Cubes
A cube object 3”*3”*3” is painted with green in
all the outer surfaces. If the cube is cut into
cubes of 1”*1”*1”, how many 1” cubes will
have at least one surface painted?
Cubes
Answer:
3*3*3 = 27
All the outer surface are painted with colour.
26 One inch cubes are painted at least one
surface.
Cubes
A cube of 12 mm is painted on all its sides. If it
is made up of small cubes of size 3mm, and if
the big cube is split into those small cubes, the
number of cubes that remain unpainted is
Cubes
Answer:
= 8
Cubes
A cube of side 5 cm is divided into 125 cubes
of equal size. It is painted on all 6 sides.
1. How many cubes are coloured on only one
side?
2. How many cubes are coloured on only two
side?
3. How many cubes are coloured on only three
side?
4. How many cubes are not coloured?
Cubes
Answer:
1. 54
2. 36
3. 8
4. 27
Cubes
A cube of 4 cm is divided into 64 cubes of
equal size. One side and its opposite side is
coloured painted with orange. A side adjacent
to this and opposite side is coloured red. A side
adjacent to this and opposite side is coloured
green?
Cont..
Cubes
1. How many cubes are coloured with Red alone?
2. How many cubes are coloured orange and Red
alone?
3. How many cubes are coloured with three different
colours?
4. How many cubes are not coloured?
5. How many cubes are coloured green and Red
alone?
Cubes
Answer:
1. 8
2. 8
3. 8
4. 8
5. 8
Cubes
A 10*10*10 cube is split into small cubes of equal size
2*2*2 each. A side and adjacent to it is coloured
Pink. A side adjacent to Pink and opposite side is
coloured Blue. The remaining sides are coloured
yellow.
1. Find the no. of cubes not coloured?
2. Find the no. of cubes coloured blue alone?
3. Find the no. of cubes coloured blue & pink &
yellow?
4. Find the no. of cubes coloured blue & pink ?
5. Find the no. of cubes coloured yellow & pink ?
Cubes
Answer:
1. 27
2. 18
3. 4
4. 12
5. 12
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.