Page 1 of - emahendras.orgemahendras.org/downlods/Digi-Notes-22-01-2016-Maths-New.pdf · Page 2 of 17 Preface The Digi-Notes (Problems on Ages) as presented here is prepared strictly

Page 1 of 17

Page 2 of 17

Preface

The Digi-Notes (Problems on Ages) as presented here is prepared

strictly according to IBPS-PO, IBPS-Clerk, IBPS-SO and other PO/Clerk

level competitive exams. The main aim of the Digi-notes is to develop

the notion of the Ratio and Proportion so that candidate would be

able to handle the quantitative problems of the real world easily and

conveniently and hence in their competitive exams. Candidates are

advised to handle the Digi-Notes by keeping in mind that they are

going to LEARN (NOT STUDY) the Ratio/Proportion so that you;

yourself would be able to minimize the steps required to conclude the

answer of the question and hence develop the SHORT TRICKS.

All the best…

Page 3 of 17

Contents

1. Preface…………………………………………………………………………2

2. Contents………………………………………………………………………3

3. Introduction ………………………………………………………………..4

4. How to Handle The Age’s Question ……………………………..4

5. Problems …………………………………………………………………….5

Page 4 of 17

Introduction:

The problem based on ages is purely based on your ability to

handle the linear Equation. There are some situations in which

the ages of two or more persons is compared (with the help of

ratio or Fraction or Percentage); then in that case; we could

correlate the entire situation to the short tricks of Ratio (Some

of which are discussed in the upcoming sections)

The main challenge in handling the Age’s questions is your

ability to bifurcate that which data is of Present; which one is of

Past and which one is of Future.

How to handle The Age’s Questions:

1. If the ages of two or more persons are compared; use the

short tricks which you learned in the Ratio/Proportion Digi-

Notes.

2. If not compared; use the techniques of Simultaneous

Linear Equations to conclude the answer.

Page 5 of 17

Q.1. The age of the father 3 years ago was 7 times the age of his

son. At present the father’s age is 5 times that of his son. What

are the present ages of the father and the son?

𝟑 YEARS

𝑭 : 𝑺 = 7 : 1 𝑭 : 𝑺 = 5 : 1

𝑭 : 𝑺 = 28 : 4 𝑭 : 𝑺 = 30 : 6

yearsS

yearsF

years

962

36

45302

330

2

31

32

Page 6 of 17

Q.2. At present the age of the father is 5 times that of the age of

his son. 3 years after, the father’s age would be 4 times that of his

son. Find the present ages of the father and the son.

yearsS

yearsF

9333

4531515

31

Q.3. 3 years before the father was 7 times as old as his son.

Three years after the father’s age would be 4 times that of his

son. What are the present ages of the father and the son?

𝟑 YEARS

𝑭 : 𝑺 = 5 : 1 𝑭 : 𝑺 = 4 : 1

𝑭 : 𝑺 = 15 : 3 𝑭 : 𝑺 = 16 : 4

𝟑 YEARS

𝑭 : 𝑺 = 7 : 1 𝑭 : 𝑺 = 4 : 1

𝑭 : 𝑺 = 21 : 3 𝑭 : 𝑺 = 24 : 6

𝟑 YEARS 𝟑 YEARS

Page 7 of 17

.93.933

.453 .42

32121

yrsyrsyrsS

yrsyrsyrs

F

Q.4. The age of a man is 4 times that of his son. 5 years ago, the

man was 9 times as old as his son was at that time. What is the

present age of the man?

.3213232

.11

.55

yrsM

yrs

yrs

years

years

32

61

63

𝟓 YEARS

𝑴 : 𝑺 = 9 : 1 𝑴 : 𝑺 = 4 : 1

𝑴 : 𝑺 = 27 : 3 𝑴 : 𝑺 = 32 : 8

Page 8 of 17

Q.5. After 5 years the age of a father will be thrice the age of

his son. Whereas 5 years ago, he was 7 times as old as his

son was. What are their present ages?

2

5

4

101

.104

yrs

.10.5.52

522

.405.352

51414

yrsyrsyrsS

yrsyrsyrsF

Q.6. 10 years ago, Sita’s mother was 4 times older than her

daughter. After 10 years, the mother will be twice older than the

daughter. What is the present age of Sita?

𝟓 YEARS

𝑭 : 𝑺 = 7 : 1 𝑭 : 𝑺 = 3 : 1

𝑭 : 𝑺 = 14 : 2 𝑭 : 𝑺 = 18: 6

𝟓 YEARS

Page 9 of 17

.101

.202

yrs

yrs

.20.10.101 yrsyrsyrsD

Q.7. 1 year ago the ratio between Samir’s and Ashok’s age was

4:3. 1 year after the ratio of their ages will be 5:4. What is the

sum of their present ages in years?

.21 yrs

yrsyrsyrsAS 16214277

𝟏𝟎 YEARS

𝑴 : 𝑫 = 4 : 1 𝑴 : 𝑫 = 2 : 1

𝑴 : 𝑫 = 4 : 1 𝑴 : 𝑫 = 6: 3

𝟏𝟎 YEARS

𝟏 YEARS

𝑺 : 𝑨 = 4 : 3 𝑺 : 𝑨 = 5 : 4

𝟏 YEARS

Page 10 of 17

Q.8. 10 years ago A was half of B in age. If the ratio of their

present ages is 3:4, what will be the total of their present ages?

.35757

51

.102

yrs

yrs

yrs

Q.9. The sum of the ages of a mother and her daughter is 50

years. Also 5 years ago, the mother’s age was 7 times the age of

the daughter. What are the present ages of the mother and the

daughter?

𝟏𝟎 YEARS

𝑨 : 𝑩 = 1 : 2 𝑨 : 𝑩 = 3 : 4

𝟓 YEARS

𝑴 : 𝑫 = 7 : 1 𝑴 + 𝑫 = 50 YEARS

Page 11 of 17

.10.5.51

.405.35577

51

.408

.405550

yrsyrsyrsD

yrsyrsyrsM

yrs

yrs

yrsDM

Q.10. The sum of the ages of a son and father is 56 years. After 4

years, the age of the father will be 3 times that of the son. What

is the age of the son?

yrsSyrsyrs

yrsS

yrs

yrsSF

16.4.12

.161

.644

.644456

𝟒 YEARS

𝑭 : 𝑺 = 3 : 1 𝑭 + 𝑺 = 56 YEARS

Page 12 of 17

Q.11. The ratio of Rita’s age to the age of her mother is 3:11. The

difference of their age is 24 years. What will be the ratio of their

ages after 3 years?

3:1

36:12:

.36.3.3331111

.123.9333

.31

248

MR

yrsyrsyrsM

yrsyrsyrsR

yrs

yrs

Q.12 The ratio of the ages of the father and the son at present is 6:1.

After 5 years the ratio will become 7:2. What is the present age of the

son?

𝟑 YEARS

𝑹 : 𝑴 = 7 : 1 𝑹 ∶ 𝑴 = ?

𝑹 ~𝑴 = 24 YEARS

𝟓 YEARS

𝑭 : 𝑺 = 6 : 1 𝑭 ∶S = 7 : 2

𝑺 → 𝟏= 5 YEARS

Page 13 of 17

Q.13. A man’s age is 125% of what it was 10 years ago, but 83𝟏

𝟑% of

what it will be after 10 years. What is his present age?

.505

.101

yrs

yrs

Q.14. The ratio of present ages of A and B is 2:3. The present age of A

is 20 years. Find the age of B after 5 years?

.35.5.303

.101

.202

yrsyrsyrsB

yrs

yrs

𝑺 → 𝟏= 5 YEARS

𝟏𝟎 YEARS

𝟏𝟐𝟓

𝟏𝟎 YEARS

𝟏𝟎𝟎

𝟒 : 5

𝟐𝟓𝟎/𝟑 : 100

5 : 6

𝟓 YEARS

𝑨 : 𝑩 = 2 : 3 𝑩 = ?

𝑨= 20 YEARS

Page 14 of 17

Q.15. The present ratio of age of A and B is 3:5. If the sum of present

age of A and B is 48 years. Find the ages of A and B before 5 years.

.61

.488

yrs

yrs

.306555.25

.186335.13

yrsByrsyrs

yrsAyrsyrs

Q.16. The ratio of ages of A and B before 5 years was 2:3. If

the sum of ages of A and B at present is 45 years. Find the

present ages of A and B.

𝟓 YEARS

𝑨 : 𝑩 = 3 : 5 A + B = 48 YEARS

A = ? B = ?

𝟓 YEARS

A + B = 45 YEARS A = ? , B = ?

𝑨 ∶ 𝑩 = 𝟐 ∶ 𝟑

Page 15 of 17

Q.17. Jayesh is as younger to Amit as he is older to Prashant. If the

sum of the ages of Amit and Prashant is 48 years. What is the age of

Jayesh in years?

.24

.482

2

yrsJ

yrsJ

PAJ

PJJA

Q.18. The age of a girl is half of the age of her father and twice the

age of the brother. 12 years after, the age of the brother would be

half of the age of the father. Find the present age of the girl.

𝑨 ∶ 𝑩 = 𝟐 ∶ 𝟑

𝟏𝟐 YEARS

F:G = 2:1 G:B = 2:1

F:B = 2:1

.26.5.213

.19.5.142

.71

.355

.355545

yrsyrsyrsB

yrsyrsyrsA

yrs

yrs

yrsBA

Page 16 of 17

yrs. G

: :

: F:B :F:B

: F:B ::F:G:B

122

3614

1214

12124

Q.19. Vimla is got married 24 years ago. Her age at present if 3 times

of the age when she got married. At present her age is 12/5thtimes

that of the age of the son. Find the present age of the son.

.155

.31

.3612

.363

.121

.242

yrs

yrs

yrs

Again

yrs

yrs

yrs

𝟐𝟒 YEARS

V:S = 12:5 S = ?

𝟏 : 3

Page 17 of 17

Q.20. The ratio of the ages of A and B at present is 3:4. The age of B 6

years after will be 26 years. C is 8 years younger than A. Find the

present age of C’s father who is 21 years older than him.

.28217

.7815

.153

.51

.204

.20626

yrsF

yrsC

yrsA

yrs

yrs

yrsB

𝟔 YEARS

A:B = 3:4 A – C = 8 YEARS F = C + 21 YEARS

𝐁 = 𝟐𝟔 YEARS