SlideShare a Scribd company logo
1 of 34
Download to read offline
Problemson Ages
Content
1) Introduction
2) Forming equations
3) Solving the questions by using general equation
4) Solving the questions by using tricks
5) Practice problems
6) Problems on numbers
i. Multiple of the ratio
ii. Ratio difference
iii. Divisible values
iv. Change in ratio
v. Different timeline
1) INTRODUCTION
It is easy to solve all these problems by equations but your
objective in exam should be solving these problems in the
easiest way which saves more than half the time compared to
solving by equation.
The easiest way in solving these questions will be by picking
the right answer among the four options using the ratio or
the values given in the question.
2) Forming equations
Statement Equation
A’s age 3 years later (after / hence / down the line) A+3
A’s age 3 years ago A-3
A is 3 years older than B A = B + 3
A is 3 years younger than B A = B - 3
A is 3 times (thrice) as old as B A = 3B
A is 3 times older than B (or)
A is 3 times older to B
A = B + 3B =>
A = 4B
Father was as old as his son at present, at the time of
his birth.
F - S = S =>
F = 2S
The present age ratio of A and B is 5:6.
Four years hence (or after) their age ratio will be 6:7.
A/B = 5/6
(A+4) / (B+4) = 6:7.
3) Solving the questions by using GENERAL EQUATION
Example: The sum of the present ages of a son and his
father is 60 years. Six years ago, father's age was five times
the age of the son. After 6 years, what will be son's age?
S+F = 60
F-6 = 5(S-6)
S+6 = ?
Eq 2 becomes F-6 = 5S – 30
F = 5S – 24
Substitute this is Eq 1: S + F = 60
S + (5S – 24) = 60
6S = 84
S = 14
S+6 = 20
∴ The age of the son after 6 years is 20
4) Solving the question by using TRICKS
Avoid using variables x & y always as there is a chance of
going wrong in relating the variables with the persons given.
Instead, using the first letter will make the relating easy.
For example S can be used as son’s age and F can be used as
father’s age.
Trick 1: Multiple of the ratio
Example: Present ages of Kiran and Shyam are in the ratio
of 5 : 4 respectively. Three years hence, the ratio of their
ages will become 11 : 9 respectively. What is Shyam's
present age in years?
A. 24
B. 22
C. 26
D. 28
Now: The age of Kiran and Shyam is in the ratio 5:4.
∴ Shyam’s age should be in the multiple of 4.
Only option a and d are having the age of Shyam in the
multiple of 4. The answer should be either a)24 or d)28.
After 3 years:
Kiran’s age – a)24+3=27 or d)28+3=31
The age of Kiran and Shyam will be in the ratio 11:9.
∴ Shyam’s age should be in the multiple of 9.
Only a)27 is in the multiple of 9.
∴ Shyam’s present age is a)24.
Example 1. One year ago, the ratio of Sooraj's and
Vimal's age was 6: 7 respectively. Four years hence, this
ratio would become 7: 8. How old is Vimal?
A.44Years
B.43 years
C.49 Years
D.36 Years
Trick 2: Ratio difference
Example: Alan is younger than Turing by 6 years and their
ages are in the respective ratio of 7 : 9, how old is Turing?
A. 18
B. 27
C. 35
D. 36
The age of Alan and Turing is in the ratio 7:9.
The age difference between them is 6.
Equate the ratio difference and age difference
7:9
2 parts
6
2 parts = 6
1 part = 3
9 parts = 27
∴ The age of Turing is 27
Example 2. The ratio between the present ages of P and Q
is 6:7. If Q is 4 years old than P, what will be the ratio of
the ages of P and Q after 4 years.
A)7:9
B)3:8
C)7:8
D)5:8
Trick 3: Divisible values
Example: A person's present age is two-fifth of the age of his
mother. After 8 years, he will be one-half of the age of his
mother. What is the present age of the mother?
A. 62
B. 45
C. 40
D. 56
Now: P= 2/5 M
This indicates that M should be divisible by 5.
Only options b) 45 and c) 40 are divisible by 5.
After 8 years:
M+8= b) 45+8 = 53 or c)40+8 = 48
P+8 = ½(M+8)
This indicates that M+8 should be divisible by 2.
Only option c)48 is divisible by 2.
∴ Mother’s age is c) 40
Example 3. Sandeep's age after six years will be three-
seventh of his father's age. Ten years ago the ratio of
their ages was 1 : 5. What is Sandeep's father's age at
present?
A. 43 Years
B. 60Years
C. 50 Years
D. 56 Years
Trick 4: Change in ratio
Example: Father is aged three times more than his son
Sunil. After 8 years, he would be two and a half times of
Sunil's age. After further 8 years, how many times would he
be of Sunil's age?
A. 2 times
B. 3 times
C. 4 times
D. 5 times
Now : F:S = 3:1
After 8 years : F:S = 2½:1
After 16 years: ?
As the years passes the ratio of the ages will always
decrease.
So after 16 years the ratio should be < 2½ :1
Only option a) 2 is less than 2½
Trick 5 : Different timeline
Example: Ayesha's father was 38 years of age when she
was born while her mother was 36 years old when her
brother four years younger to her was born. What is the
difference between the ages of her parents?
A. 6 Years
B. 5 Years
C. 7 Years
D. 6.5 Years
Ayesha's Father was 38 years old when she was born
F A
38 0
Her Mother was 36 years old when her Brother was born.
M B
360
Her Brother is four years younger to her
B A
0 4
As these three equations are not in the same timeline, compare the
values and make it same.
Eq 2 & Eq 3: The common value B is already same.
Eq 1 & Eq 3: A=0 & A=4. To make it equal add 4 with eq1.
F A
424
∴ F A M B
42 4 36 0
The difference between F and M is 6.
Example 5. A father said to his son, "I was as old as you
are at the present at the time of your birth". If the
father's age is 38 years now, what was the son's age five
years back?
A.14 Years
B.15 Years
C.16 Years
D.18 Years
5) Practice problems
Q1. The total age of A and B is 12 years more than the
total age of B and C. C is how many year younger than
A?
A.12
B.13
C.14
D.15
Q2.The sum of ages of 5 children born at the intervals
of 3 years each is 50 years. What is the age of the
youngest child?
A.2
B.4
C.6
D.10
Q3.Ages of two person differ by 16 years. If 6 year ago,
the elder one be 3 times as old the younger one, find
their present age.
A.36, 16
B.30, 14
C.24, 8
D.30, 10
Q4. Steve is older than Mark by 6 years. If the ratio of
their current ages is 7:9, what will be the corresponding
new ratio of their ages when Mark is twice as old as he
is now?
A.7:8
B.4:7
C.3:9
D.1:4
Problems On Numbers
Some Basic Formulae:
(a + b)(a - b) = (a2 - b2)
(a + b)2 = (a2 + b2 + 2ab)
(a - b)2 = (a2 + b2 - 2ab)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
(a3 + b3) = (a + b)(a2 - ab + b2)
(a3 - b3) = (a - b)(a2 + ab + b2)
(a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc -
ac)
When a + b + c = 0, then a3 + b3 + c3 = 3abc.
A two digit number can be represented as 10x+y where x
and y are the two digits.
Similarly a three digit number as 100x+10y+z and so on.
Q1. If one-third of one-fourth of a number is 15, then
three-tenth of that number is:
A.54
B.45
C.36
D.58
Q2. The difference between a two-digit number and the
number obtained by interchanging the digits is 36.
What is the difference between the sum and the
difference of the digits of the number if the ratio
between the digits of the number is 1 : 2 ?
A.8
B.16
C.4
D.12
Q3. Three times the first of three consecutive odd
integers is 3 more than twice the third. The third integer
is:
A.15
B.14
C.12
D.17
Q4. A two-digit number is such that the product of the
digits is 8. When 18 is added to the number, then the
digits are reversed. The number is:
A.24
B.12
C.48
D.26
Q5. In a two-digit, if it is known that its unit's digit
exceeds its ten's digit by 2 and that the product of the
given number and the sum of its digits is equal to 144,
then the number is:
A.24
B.26
C.28
D.30
E.32
19848_pea-300_problems-on-ages-and-numbers.ppt

More Related Content

Similar to 19848_pea-300_problems-on-ages-and-numbers.ppt

Teoria y problemas de razones y proporciones RP24 ccesa007
Teoria y problemas de razones y proporciones RP24 ccesa007Teoria y problemas de razones y proporciones RP24 ccesa007
Teoria y problemas de razones y proporciones RP24 ccesa007Demetrio Ccesa Rayme
 
Teoría y problemas de razones y proporciones RP24 ccesa007
Teoría y problemas de razones y proporciones RP24 ccesa007Teoría y problemas de razones y proporciones RP24 ccesa007
Teoría y problemas de razones y proporciones RP24 ccesa007Demetrio Ccesa Rayme
 
Quantitative Aptitude
Quantitative AptitudeQuantitative Aptitude
Quantitative Aptituderavikant7883
 
Age Problems (4).pdf
Age Problems (4).pdfAge Problems (4).pdf
Age Problems (4).pdfNoraima2
 
Algebra "Age Problem"
Algebra "Age Problem"Algebra "Age Problem"
Algebra "Age Problem"guestc71130
 
Aptitude Training - AGES
Aptitude Training - AGESAptitude Training - AGES
Aptitude Training - AGESAjay Chimmani
 
Competitive Mathematics Model Question Paper || Sourav Sir's Classes
Competitive Mathematics Model Question Paper || Sourav Sir's ClassesCompetitive Mathematics Model Question Paper || Sourav Sir's Classes
Competitive Mathematics Model Question Paper || Sourav Sir's ClassesSOURAV DAS
 
Competitive mathematics ques paper BY SOURAV SIR'S CLASSES
Competitive mathematics ques paper BY SOURAV SIR'S CLASSES Competitive mathematics ques paper BY SOURAV SIR'S CLASSES
Competitive mathematics ques paper BY SOURAV SIR'S CLASSES SOURAV DAS
 
Mega pp -_v1
Mega pp -_v1Mega pp -_v1
Mega pp -_v1harlie90
 
Ratio and Two Variable Problems
Ratio and Two Variable ProblemsRatio and Two Variable Problems
Ratio and Two Variable ProblemsGeorge Prep
 
Lesson on Ratio and Proportion.pptx
Lesson on Ratio and Proportion.pptxLesson on Ratio and Proportion.pptx
Lesson on Ratio and Proportion.pptxReahRomero3
 
Triangle inequality (sides)
Triangle inequality (sides)Triangle inequality (sides)
Triangle inequality (sides)jmui
 
Triangle inequality (sides)
Triangle inequality (sides)Triangle inequality (sides)
Triangle inequality (sides)jmui
 
primary maths p5- igcse collection
primary maths  p5- igcse collectionprimary maths  p5- igcse collection
primary maths p5- igcse collection8008975725
 
Quiz linear equation in one variable
Quiz linear equation in one variableQuiz linear equation in one variable
Quiz linear equation in one variablePooja M
 

Similar to 19848_pea-300_problems-on-ages-and-numbers.ppt (20)

Linear equations
Linear equationsLinear equations
Linear equations
 
Teoria y problemas de razones y proporciones RP24 ccesa007
Teoria y problemas de razones y proporciones RP24 ccesa007Teoria y problemas de razones y proporciones RP24 ccesa007
Teoria y problemas de razones y proporciones RP24 ccesa007
 
Teoría y problemas de razones y proporciones RP24 ccesa007
Teoría y problemas de razones y proporciones RP24 ccesa007Teoría y problemas de razones y proporciones RP24 ccesa007
Teoría y problemas de razones y proporciones RP24 ccesa007
 
Quantitative Aptitude
Quantitative AptitudeQuantitative Aptitude
Quantitative Aptitude
 
Age Problems (4).pdf
Age Problems (4).pdfAge Problems (4).pdf
Age Problems (4).pdf
 
Age_Problems_(4).pdf
Age_Problems_(4).pdfAge_Problems_(4).pdf
Age_Problems_(4).pdf
 
Algebra "Age Problem"
Algebra "Age Problem"Algebra "Age Problem"
Algebra "Age Problem"
 
Aptitude Training - AGES
Aptitude Training - AGESAptitude Training - AGES
Aptitude Training - AGES
 
Competitive Mathematics Model Question Paper || Sourav Sir's Classes
Competitive Mathematics Model Question Paper || Sourav Sir's ClassesCompetitive Mathematics Model Question Paper || Sourav Sir's Classes
Competitive Mathematics Model Question Paper || Sourav Sir's Classes
 
Competitive mathematics ques paper BY SOURAV SIR'S CLASSES
Competitive mathematics ques paper BY SOURAV SIR'S CLASSES Competitive mathematics ques paper BY SOURAV SIR'S CLASSES
Competitive mathematics ques paper BY SOURAV SIR'S CLASSES
 
Mega pp -_v1
Mega pp -_v1Mega pp -_v1
Mega pp -_v1
 
Ratio and Two Variable Problems
Ratio and Two Variable ProblemsRatio and Two Variable Problems
Ratio and Two Variable Problems
 
Apttitude
ApttitudeApttitude
Apttitude
 
Lesson on Ratio and Proportion.pptx
Lesson on Ratio and Proportion.pptxLesson on Ratio and Proportion.pptx
Lesson on Ratio and Proportion.pptx
 
Naren Quiz 14 Dr.K.Karthikeyan
Naren Quiz 14 Dr.K.KarthikeyanNaren Quiz 14 Dr.K.Karthikeyan
Naren Quiz 14 Dr.K.Karthikeyan
 
Triangle inequality (sides)
Triangle inequality (sides)Triangle inequality (sides)
Triangle inequality (sides)
 
Triangle inequality (sides)
Triangle inequality (sides)Triangle inequality (sides)
Triangle inequality (sides)
 
primary maths p5- igcse collection
primary maths  p5- igcse collectionprimary maths  p5- igcse collection
primary maths p5- igcse collection
 
Quiz linear equation in one variable
Quiz linear equation in one variableQuiz linear equation in one variable
Quiz linear equation in one variable
 
Gmat math bank quant
Gmat math bank   quantGmat math bank   quant
Gmat math bank quant
 

More from CharbelRahme2

Ch 8 - Energy, Enthalpy, and Thermochemistry.pdf
Ch 8 - Energy, Enthalpy, and Thermochemistry.pdfCh 8 - Energy, Enthalpy, and Thermochemistry.pdf
Ch 8 - Energy, Enthalpy, and Thermochemistry.pdfCharbelRahme2
 
Ch 2 - The Structure of Atoms.pdf
Ch 2 - The Structure of Atoms.pdfCh 2 - The Structure of Atoms.pdf
Ch 2 - The Structure of Atoms.pdfCharbelRahme2
 
Ch 1 - Fundamentals 7th ed.pdf
Ch 1 - Fundamentals  7th ed.pdfCh 1 - Fundamentals  7th ed.pdf
Ch 1 - Fundamentals 7th ed.pdfCharbelRahme2
 
Solving-Sales-and-Marketing-Alignment.pdf
Solving-Sales-and-Marketing-Alignment.pdfSolving-Sales-and-Marketing-Alignment.pdf
Solving-Sales-and-Marketing-Alignment.pdfCharbelRahme2
 
GE Digital - Customer Reference Stories - 9Nov2017.pptx
GE Digital - Customer Reference Stories - 9Nov2017.pptxGE Digital - Customer Reference Stories - 9Nov2017.pptx
GE Digital - Customer Reference Stories - 9Nov2017.pptxCharbelRahme2
 
abb-form-and-strategy-created-by816.ppt
abb-form-and-strategy-created-by816.pptabb-form-and-strategy-created-by816.ppt
abb-form-and-strategy-created-by816.pptCharbelRahme2
 
final2abbgrouppresentation2013en-150524090737-lva1-app6892.ppt
final2abbgrouppresentation2013en-150524090737-lva1-app6892.pptfinal2abbgrouppresentation2013en-150524090737-lva1-app6892.ppt
final2abbgrouppresentation2013en-150524090737-lva1-app6892.pptCharbelRahme2
 
50_most_famous_people_who_got_success_but1.pptx
50_most_famous_people_who_got_success_but1.pptx50_most_famous_people_who_got_success_but1.pptx
50_most_famous_people_who_got_success_but1.pptxCharbelRahme2
 
Understanding the RF Path
Understanding the RF PathUnderstanding the RF Path
Understanding the RF PathCharbelRahme2
 

More from CharbelRahme2 (13)

11715660.ppt
11715660.ppt11715660.ppt
11715660.ppt
 
V_Tikhvinskiy.pdf
V_Tikhvinskiy.pdfV_Tikhvinskiy.pdf
V_Tikhvinskiy.pdf
 
Ch 8 - Energy, Enthalpy, and Thermochemistry.pdf
Ch 8 - Energy, Enthalpy, and Thermochemistry.pdfCh 8 - Energy, Enthalpy, and Thermochemistry.pdf
Ch 8 - Energy, Enthalpy, and Thermochemistry.pdf
 
Ch 2 - The Structure of Atoms.pdf
Ch 2 - The Structure of Atoms.pdfCh 2 - The Structure of Atoms.pdf
Ch 2 - The Structure of Atoms.pdf
 
Ch 1 - Fundamentals 7th ed.pdf
Ch 1 - Fundamentals  7th ed.pdfCh 1 - Fundamentals  7th ed.pdf
Ch 1 - Fundamentals 7th ed.pdf
 
Solving-Sales-and-Marketing-Alignment.pdf
Solving-Sales-and-Marketing-Alignment.pdfSolving-Sales-and-Marketing-Alignment.pdf
Solving-Sales-and-Marketing-Alignment.pdf
 
GE Digital - Customer Reference Stories - 9Nov2017.pptx
GE Digital - Customer Reference Stories - 9Nov2017.pptxGE Digital - Customer Reference Stories - 9Nov2017.pptx
GE Digital - Customer Reference Stories - 9Nov2017.pptx
 
abb-form-and-strategy-created-by816.ppt
abb-form-and-strategy-created-by816.pptabb-form-and-strategy-created-by816.ppt
abb-form-and-strategy-created-by816.ppt
 
final2abbgrouppresentation2013en-150524090737-lva1-app6892.ppt
final2abbgrouppresentation2013en-150524090737-lva1-app6892.pptfinal2abbgrouppresentation2013en-150524090737-lva1-app6892.ppt
final2abbgrouppresentation2013en-150524090737-lva1-app6892.ppt
 
Jazz.pdf
Jazz.pdfJazz.pdf
Jazz.pdf
 
Mind Maps.pptx
Mind Maps.pptxMind Maps.pptx
Mind Maps.pptx
 
50_most_famous_people_who_got_success_but1.pptx
50_most_famous_people_who_got_success_but1.pptx50_most_famous_people_who_got_success_but1.pptx
50_most_famous_people_who_got_success_but1.pptx
 
Understanding the RF Path
Understanding the RF PathUnderstanding the RF Path
Understanding the RF Path
 

Recently uploaded

6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroomSamsung Business USA
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...Nguyen Thanh Tu Collection
 
Sarah Lahm In Media Res Media Component
Sarah Lahm  In Media Res Media ComponentSarah Lahm  In Media Res Media Component
Sarah Lahm In Media Res Media ComponentInMediaRes1
 
How to Share Dashboard in the Odoo 17 ERP
How to Share Dashboard in the Odoo 17 ERPHow to Share Dashboard in the Odoo 17 ERP
How to Share Dashboard in the Odoo 17 ERPCeline George
 
(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf
(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf
(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdfMJDuyan
 
Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024
Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024
Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024St.John's College
 
647291105-Ppt-Arts-10-4th-Quarter-1.pdfi
647291105-Ppt-Arts-10-4th-Quarter-1.pdfi647291105-Ppt-Arts-10-4th-Quarter-1.pdfi
647291105-Ppt-Arts-10-4th-Quarter-1.pdfijoemmbrillantes
 
Shark introduction Morphology and its behaviour characteristics
Shark introduction Morphology and its behaviour characteristicsShark introduction Morphology and its behaviour characteristics
Shark introduction Morphology and its behaviour characteristicsArubSultan
 
4.9.24 School Desegregation in Boston.pptx
4.9.24 School Desegregation in Boston.pptx4.9.24 School Desegregation in Boston.pptx
4.9.24 School Desegregation in Boston.pptxmary850239
 
HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...
HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...
HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...kumarpriyanshu81
 
PART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFE
PART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFEPART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFE
PART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFEMISSRITIMABIOLOGYEXP
 
4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptx4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptxmary850239
 
BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...
BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...
BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...Nguyen Thanh Tu Collection
 
Views in Odoo 17 - Kanban View in odoo 17
Views in Odoo 17 - Kanban View  in odoo 17Views in Odoo 17 - Kanban View  in odoo 17
Views in Odoo 17 - Kanban View in odoo 17Celine George
 
Self directed Learning - SDL, introduction to SDL
Self directed Learning - SDL, introduction to SDLSelf directed Learning - SDL, introduction to SDL
Self directed Learning - SDL, introduction to SDLspmdoc
 
Transdisciplinary Pathways for Urban Resilience [Work in Progress].pptx
Transdisciplinary Pathways for Urban Resilience [Work in Progress].pptxTransdisciplinary Pathways for Urban Resilience [Work in Progress].pptx
Transdisciplinary Pathways for Urban Resilience [Work in Progress].pptxinfo924062
 
4.4.24 Economic Precarity and Global Economic Forces.pptx
4.4.24 Economic Precarity and Global Economic Forces.pptx4.4.24 Economic Precarity and Global Economic Forces.pptx
4.4.24 Economic Precarity and Global Economic Forces.pptxmary850239
 
Jason Potel In Media Res Media Component
Jason Potel In Media Res Media ComponentJason Potel In Media Res Media Component
Jason Potel In Media Res Media ComponentInMediaRes1
 

Recently uploaded (20)

6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
 
Sarah Lahm In Media Res Media Component
Sarah Lahm  In Media Res Media ComponentSarah Lahm  In Media Res Media Component
Sarah Lahm In Media Res Media Component
 
How to Share Dashboard in the Odoo 17 ERP
How to Share Dashboard in the Odoo 17 ERPHow to Share Dashboard in the Odoo 17 ERP
How to Share Dashboard in the Odoo 17 ERP
 
(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf
(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf
(Part 3) CHILDREN'S DISABILITIES AND EXCEPTIONALITIES.pdf
 
Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024
Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024
Basic cosmetics prepared by my student Mr. Balamurugan, II Maths, 2023-2024
 
647291105-Ppt-Arts-10-4th-Quarter-1.pdfi
647291105-Ppt-Arts-10-4th-Quarter-1.pdfi647291105-Ppt-Arts-10-4th-Quarter-1.pdfi
647291105-Ppt-Arts-10-4th-Quarter-1.pdfi
 
Shark introduction Morphology and its behaviour characteristics
Shark introduction Morphology and its behaviour characteristicsShark introduction Morphology and its behaviour characteristics
Shark introduction Morphology and its behaviour characteristics
 
Israel Genealogy Research Assoc. April 2024 Database Release
Israel Genealogy Research Assoc. April 2024 Database ReleaseIsrael Genealogy Research Assoc. April 2024 Database Release
Israel Genealogy Research Assoc. April 2024 Database Release
 
4.9.24 School Desegregation in Boston.pptx
4.9.24 School Desegregation in Boston.pptx4.9.24 School Desegregation in Boston.pptx
4.9.24 School Desegregation in Boston.pptx
 
HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...
HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...
HackerOne X IoT Lab Bug Bounty 101 with Encryptsaan & IoT Lab at KIIT Univers...
 
PART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFE
PART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFEPART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFE
PART 1 - CHAPTER 1 - CELL THE FUNDAMENTAL UNIT OF LIFE
 
CARNAVAL COM MAGIA E EUFORIA _
CARNAVAL COM MAGIA E EUFORIA            _CARNAVAL COM MAGIA E EUFORIA            _
CARNAVAL COM MAGIA E EUFORIA _
 
4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptx4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptx
 
BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...
BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...
BÀI TẬP BỔ TRỢ 4 KĨ NĂNG TIẾNG ANH LỚP 8 - CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC ...
 
Views in Odoo 17 - Kanban View in odoo 17
Views in Odoo 17 - Kanban View  in odoo 17Views in Odoo 17 - Kanban View  in odoo 17
Views in Odoo 17 - Kanban View in odoo 17
 
Self directed Learning - SDL, introduction to SDL
Self directed Learning - SDL, introduction to SDLSelf directed Learning - SDL, introduction to SDL
Self directed Learning - SDL, introduction to SDL
 
Transdisciplinary Pathways for Urban Resilience [Work in Progress].pptx
Transdisciplinary Pathways for Urban Resilience [Work in Progress].pptxTransdisciplinary Pathways for Urban Resilience [Work in Progress].pptx
Transdisciplinary Pathways for Urban Resilience [Work in Progress].pptx
 
4.4.24 Economic Precarity and Global Economic Forces.pptx
4.4.24 Economic Precarity and Global Economic Forces.pptx4.4.24 Economic Precarity and Global Economic Forces.pptx
4.4.24 Economic Precarity and Global Economic Forces.pptx
 
Jason Potel In Media Res Media Component
Jason Potel In Media Res Media ComponentJason Potel In Media Res Media Component
Jason Potel In Media Res Media Component
 

19848_pea-300_problems-on-ages-and-numbers.ppt

  • 2. Content 1) Introduction 2) Forming equations 3) Solving the questions by using general equation 4) Solving the questions by using tricks 5) Practice problems 6) Problems on numbers i. Multiple of the ratio ii. Ratio difference iii. Divisible values iv. Change in ratio v. Different timeline
  • 3. 1) INTRODUCTION It is easy to solve all these problems by equations but your objective in exam should be solving these problems in the easiest way which saves more than half the time compared to solving by equation. The easiest way in solving these questions will be by picking the right answer among the four options using the ratio or the values given in the question.
  • 4. 2) Forming equations Statement Equation A’s age 3 years later (after / hence / down the line) A+3 A’s age 3 years ago A-3 A is 3 years older than B A = B + 3 A is 3 years younger than B A = B - 3 A is 3 times (thrice) as old as B A = 3B A is 3 times older than B (or) A is 3 times older to B A = B + 3B => A = 4B Father was as old as his son at present, at the time of his birth. F - S = S => F = 2S The present age ratio of A and B is 5:6. Four years hence (or after) their age ratio will be 6:7. A/B = 5/6 (A+4) / (B+4) = 6:7.
  • 5. 3) Solving the questions by using GENERAL EQUATION Example: The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age? S+F = 60 F-6 = 5(S-6) S+6 = ? Eq 2 becomes F-6 = 5S – 30 F = 5S – 24 Substitute this is Eq 1: S + F = 60 S + (5S – 24) = 60 6S = 84 S = 14 S+6 = 20 ∴ The age of the son after 6 years is 20
  • 6. 4) Solving the question by using TRICKS Avoid using variables x & y always as there is a chance of going wrong in relating the variables with the persons given. Instead, using the first letter will make the relating easy. For example S can be used as son’s age and F can be used as father’s age.
  • 7. Trick 1: Multiple of the ratio Example: Present ages of Kiran and Shyam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Shyam's present age in years? A. 24 B. 22 C. 26 D. 28
  • 8. Now: The age of Kiran and Shyam is in the ratio 5:4. ∴ Shyam’s age should be in the multiple of 4. Only option a and d are having the age of Shyam in the multiple of 4. The answer should be either a)24 or d)28. After 3 years: Kiran’s age – a)24+3=27 or d)28+3=31 The age of Kiran and Shyam will be in the ratio 11:9. ∴ Shyam’s age should be in the multiple of 9. Only a)27 is in the multiple of 9. ∴ Shyam’s present age is a)24.
  • 9. Example 1. One year ago, the ratio of Sooraj's and Vimal's age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Vimal? A.44Years B.43 years C.49 Years D.36 Years
  • 10. Trick 2: Ratio difference Example: Alan is younger than Turing by 6 years and their ages are in the respective ratio of 7 : 9, how old is Turing? A. 18 B. 27 C. 35 D. 36
  • 11. The age of Alan and Turing is in the ratio 7:9. The age difference between them is 6. Equate the ratio difference and age difference 7:9 2 parts 6 2 parts = 6 1 part = 3 9 parts = 27 ∴ The age of Turing is 27
  • 12. Example 2. The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years. A)7:9 B)3:8 C)7:8 D)5:8
  • 13. Trick 3: Divisible values Example: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of the mother? A. 62 B. 45 C. 40 D. 56
  • 14. Now: P= 2/5 M This indicates that M should be divisible by 5. Only options b) 45 and c) 40 are divisible by 5. After 8 years: M+8= b) 45+8 = 53 or c)40+8 = 48 P+8 = ½(M+8) This indicates that M+8 should be divisible by 2. Only option c)48 is divisible by 2. ∴ Mother’s age is c) 40
  • 15. Example 3. Sandeep's age after six years will be three- seventh of his father's age. Ten years ago the ratio of their ages was 1 : 5. What is Sandeep's father's age at present? A. 43 Years B. 60Years C. 50 Years D. 56 Years
  • 16. Trick 4: Change in ratio Example: Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil's age. After further 8 years, how many times would he be of Sunil's age? A. 2 times B. 3 times C. 4 times D. 5 times
  • 17. Now : F:S = 3:1 After 8 years : F:S = 2½:1 After 16 years: ? As the years passes the ratio of the ages will always decrease. So after 16 years the ratio should be < 2½ :1 Only option a) 2 is less than 2½
  • 18. Trick 5 : Different timeline Example: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? A. 6 Years B. 5 Years C. 7 Years D. 6.5 Years
  • 19. Ayesha's Father was 38 years old when she was born F A 38 0 Her Mother was 36 years old when her Brother was born. M B 360 Her Brother is four years younger to her B A 0 4 As these three equations are not in the same timeline, compare the values and make it same. Eq 2 & Eq 3: The common value B is already same. Eq 1 & Eq 3: A=0 & A=4. To make it equal add 4 with eq1. F A 424 ∴ F A M B 42 4 36 0 The difference between F and M is 6.
  • 20. Example 5. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, what was the son's age five years back? A.14 Years B.15 Years C.16 Years D.18 Years
  • 22. Q1. The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A? A.12 B.13 C.14 D.15
  • 23. Q2.The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? A.2 B.4 C.6 D.10
  • 24. Q3.Ages of two person differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age. A.36, 16 B.30, 14 C.24, 8 D.30, 10
  • 25. Q4. Steve is older than Mark by 6 years. If the ratio of their current ages is 7:9, what will be the corresponding new ratio of their ages when Mark is twice as old as he is now? A.7:8 B.4:7 C.3:9 D.1:4
  • 27. Some Basic Formulae: (a + b)(a - b) = (a2 - b2) (a + b)2 = (a2 + b2 + 2ab) (a - b)2 = (a2 + b2 - 2ab) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) (a3 + b3) = (a + b)(a2 - ab + b2) (a3 - b3) = (a - b)(a2 + ab + b2) (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac) When a + b + c = 0, then a3 + b3 + c3 = 3abc.
  • 28. A two digit number can be represented as 10x+y where x and y are the two digits. Similarly a three digit number as 100x+10y+z and so on.
  • 29. Q1. If one-third of one-fourth of a number is 15, then three-tenth of that number is: A.54 B.45 C.36 D.58
  • 30. Q2. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? A.8 B.16 C.4 D.12
  • 31. Q3. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: A.15 B.14 C.12 D.17
  • 32. Q4. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: A.24 B.12 C.48 D.26
  • 33. Q5. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: A.24 B.26 C.28 D.30 E.32

Editor's Notes

  1. Explanation: Let the age of Sooraj and Vimal, 1 year ago, be 6x and 7xrespectively. Given that, four years hence, this ratio would become 7:8 ⇒(6x+5):(7x+5)=7:8 ⇒8(6x+5)=7(7x+5) ⇒48x+40=49x+35 ⇒x=5 Vimal's present age =7x+1=7×5+1=36
  2. Let P age and Q age is 6x years and 7x years. Then 7x - 6x = 4 <=> x = 4 So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
  3. Explanation: Let the age of Sandeep and his father before 10 years be x and 5x respectively. Given that Sandeep's age after six years will be three-seventh of his father's age ⇒x+16=3/7(5x+16) ⇒7x+112=15x+48 ⇒8x=64 ⇒x=8 Sandeep's father's present age =5x+10=5×8+10=50
  4. Let son's present age be xx years. Then, (38−x)=x ⇒2x=38 ⇒x=382=19 Son's age 55 years back =19−5=14
  5. Ratio difference = 9-7=2 units Age difference = 4 2 units ---------- 4 7 units --------- ? Mark age = 14  years Similarly Steve age = 18 years Mark is twice as old as he is age = 14 +14 =28 At the same time Steve age = 18+14 = 32 New ratio = 7:8