# Problems On Ages Tricks & Tips

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## Introduction:

Today we are going to discuss on AGES this is quite easy when comparing other application sums and it take just few seconds to solve the question.

And it carries 1 or 2 marks in the  Prelims as well as in Mains

There are only 3 Types of problems in ages namely:

1.Finding  Present Age

2.Finding  Previous Age(Age before some years)

3.Finding  Future Age(Age after Some years)

## BASED ON FINDING PRESENT AGE:

1.The  ages of Rahul and Amit are in the Ratio of 9:6.Their sum of the ages  be 95.Find the age of Rahul?

Explanation:

Rahul age=9X   Amit Age=6X

Sum of their Ages be(9X+6X)=15X

Rahul’s age=95*(9/15)

=57 years

2.Present Ages of Sameer and Anand are in the ratio of 5:4 respectively.Three years hence,the ratio of their ages will become 11:9 respectively.What is Anand’s  Present  age  in years?

Explanation:
 Person Present Year After 3 Year Sameer 5x 5x+3=11 Anand 4x 4x+3=9

9(5X+3)=11(4X+3)

45X+27=44X+33

X=6

Anand’s Present Age=4*6=24Years

3.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,the son’s age is?

Explanation:

Let the son’s present age be X,

Then,(38-X)=X

2X=38

X=19 years

## BASED ON EFFICIENCY:

1)A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is?

Explanation:

Let Son’s  Age=X

Man Age =24 + X

After  two years:

24 + X+2=2(X+2)

26 + X=2x+4

X=22 years

2)A is two years older than B who is twice as old as C.If the total of the ages of A,B and C be 27,then how old is B?

Explanation:
 A B C 2X+2 2X X

(2X+2) +2X + X=27

5X+2=27            5X=25             X=5

B=2X, B=2*5

B=10years.

## How to solve Problems based on Ages Part-2

### INTRODUCTION:

Problems based on Ages is the easiest topic in all the banking exams,and it is asked in Prelims and Mains Exam for 1 or 2 Mark.

There are only 3 Types of problems in ages namely

1.Finding  Present Age

2.Finding  Previous Age(Age before some years)

3.Finding  Future Age(Age after Some years)

We had discussed how to solve problems based on ages in the previous article,Click here to view how to solve problems based on Ages

Note :

If they didn’t specify the age then consider the age to be X

### FINDING AGE BEFORE SOME YEARS :

In this type we are going to assume the present age is X and to find the age before   Y  years then  Age=X-Y

1)Ganesh is 24 years younger than his Father Bholenath.3 years ago,Ganesh was 1/5 as old as his father was.What is Ganesh’s present age?

Explanation:
 Years Bholenath Ganesh Present X X-24 3 years Ago X-3 X-24-3=X-27

Before 3 years:

X-27=1/5(X-3)

5X-135=X-3

4X=132

X=33

Ganesh’s Age =(33-24)=9 Years

2.The ratio of ages of Amir and Salman is at present 3:4, 5 Years before that ratio was 2:3.What is the present age of Amir and Salman?

Explanation:
 Years Amir Salman Present Year 3X 4X 5 years ago 2 3

(3X-5)/(4X-5)=2/3   ⇒    X=5

Amir’s Present Age=15years  and Salman’s Present Age=20years

### FINDING AGES AFTER SOME YEARS:

Let the number of years be X and the age after Y  years is X+Y years

1.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. How old is the mother at present?

Explanation:

Let the present age of the mother be X years,

Then, the present age of the son is 2/5(X) years.

[2/5(X)+8]=1/2[X+8]2(2X+40)=5(X+8)

X=40

2.Ranjan’s  and  Anurag’s Age are in the ratio  4:5.4Years hence,their age ratio will become 5:6.What is Anurag’s present age?

Explanation:
 YEARS ANURAG RANJAN Present year 5 4 After 4 year 6 5

=

X=4

Anurag’s Present Age=20 years

a)16  b)20  c)25  d)30

Alternate Method(Choosing  from the option)

Ratio’s are 4:5  and  after 4 years 5:6

It is clear that Anurag age is a multiple of 4 now And after 4 yrs it is a multiple of 5

### SHORTCUT  METHOD:

When two ratio’s and after/before some years are given

Formula 1.The age of Rahul and Amit are in the ratio of  8:7.After 10 years the ratio of their Ages will be 13:12.What is the difference in years between their ages?

Explanation:

New Ratio Difference=13-12=1

Difference between old and new ratio’s Cross Multiplication

=(8/7) * (13/12)

= (96-91)=5

Present Age=(1*10)/5  = 2yrs

Difference between their age =(8*2)-(7*2)=16years-14years=2years

Age Aptitude Tricks

Type 1:

1) The ratio of Asha and Sushma are in ratio 3:4 after 8 year the ratio of their ages will be 7:8. What is difference in years between their ages?

Solution: 8 years × (difference 8-7) / (7×4) – (8×3)

= 8 × 1 / 28-24

Difference =8/4 = 2

2) 10 years ago ratio of ages of A and B was 3 : 1 and after 10 years the ratio of their ages become 2 : 1. Find the sum of present ages?

Solution: Given total years 10 and 10 so we take 20 years

20×1 / 1 = 20

A            B

10 years ago  3×20   :   1 × 20

Present age    60+10   :  20+10

Sum = 100 years

3) 5 years ago ratio of age A and B are 5 : 8 and after 5 years it will become 5 : 9 find present age? Type 2:

1). Ratio between the ages of Mother (M) and her Daughter (D) 4 years ago was 19 : 5. If difference between ages of mother and daughter is 28 years what will be the ratio of their present age? 2). 3 years ago A was 4 times as old as B. After 18 years A age will exceed B’s age by 12 years. The ratio of present ages of A and B is? 3). Divya got married 6 years ago. Today her age is 1 ¼ times her age at the time of marriage. His son age is 1/10 times her age. Age of her son is. (T) – Today Present Age Ratio

(M) – At the time of Marriage Age ratio

Type 3:

1). Five years ago the sum of the ages of Father and Son was 60 years. The ratio of present ages is 4 : 1. What is the present age of father?

Solution:

Present age of F + S = 60 + 10 = 70

F   :   S

4   :   1 ( present age)

5 –> 70

1 –> 14

Present age of F = 14 × 4 = 56 years

Type 4:

1). Sum of ages of father and son is 46 years. Seven years ago the product of their ages was 4 times the father age at that time. Find present age of father and son?

Solution:

(F-7) ×(S-7) = 4 × (F –7)

S – 7=4

S = 11 years (present)

F = 35 years (present)

Type 5:

1). Ratio of Arjun and Bhuvan age is 3 : 5. Ratio of Bhuvan and Cibi is 2 : 3. If Arjun is two fifth of Cibi what is Arjun’s age?

No one’s age is given it can’t be determined

Type 6:

1). The Average of 8 men is increased by 2 years when two of them whose ages are 21 and 23 are replaced by Two new men. The average of two new men is?

Solution:

Thus in numerator there must be changed of 16 to change average age by 2

Increase 2 years = 8 × 2 = 16

Two men = 21 + 23 = 44

= 16 +44 = 60

Average 60/2 = 30 years

2). The average age of family of 10 members is 20 years. If the age of youngest member of the family is 10 years then the average of the member of family just before the birth of youngest member was approximately?

Solution:

Here number is not constant and notion of time too

Thus total age  = 20 × 10 = 200

10 years ago = 200 (10 ×10)

= 200-100

= 100

Average = 100/9

Best way to solve Age questions is to assume fixed period with which further conditions will be compared. For example taking 2000 as fixed year.

## Application of this rule

### Example 1

Raman’s age after 15 years will be 5 times his age 5 years back. What is his present age ?

Solution – Let’s assume right now it is year 2000

Age of Raman in 1995 = x
Age of Raman in 2015 = 5x
Present age of Raman (in 2000) = x+5 or 5x-15

we will solve these two equation to find x.

X= 5. Then Raman’s present age becomes = x +5 = 10

### Example 2

Rahul was 4 times old as his son 8 years back and he will be 2 times old as his son after 8 years. Calculate Rahul and his son’s age.

Assume that currently it is year 2000.
In 1992 Rahul’s age = 4x, Age of Rahul’s son = x
In 2008 Rahul’s age = 2y and Age of Rahul’s son = y

Now we get two equations 2y – 4x = 16 and y – x = 16
By solving this equation x = 8, so Rahul’ son’s current age = 16 years and Rahul’s age = 40 years.

### Basic Concept for problems on ages :

#1. If the present age of ‘A’ is ‘x’ years, then

‘n’ years ago => Age of ‘A’ was (x-n) years.

‘n’ years after => Age of ‘A’ will be (x+n) years.

#2. In general, at the starting of the solution we have to assume the present age of one person. It is better to assume the present age = ‘x’ years.

#3. So I advise you to assume the age of the younger person = ‘x’ years.

#4. If the present age ‘A’ and ‘B’ are ‘x’ and ‘y’ years respectively, then

‘n’ years ago => Age of ‘A’ and ‘B’ were (x-n) and (y-n) years respectively.

‘n’ years after => Age of ‘A’ and ‘B’ will be (x+n) and (y+n) years respectively.

#5. The age difference between you and your friend is let’s suppose 6 years. And after 10 or 15 years this will be same, because clock will run equally for both of you. I hope you are getting what I am trying to say. : )

Q 1. Lina got married 8 years ago. Today her age is 9/7 time her age at the time of her marriage. At present her daughter’s age is 1/6 of her age. What was her daughter’s age 3 years ago?     (PNB MT 2009)

Explanation:

Let’s assume present age of Lina = x yrs.

Hence,  x = (x-8) * 9/7 => x=36 years.

So present age of daughter = 1/6 * 36 => 6 years.

3 years age of daughter = 6-3 = 3 years.

Q 2. The age of Rahul and Amit are in the ratio of 8:7. After 10 years the ratio of their ages will be 13:12. What is the difference in years between their ages?                             (UBI PO 2008)

Explanation:

Lets assume the present age of Rahul and Amit = 8x and 7x

After 10 years,

(8x+10)/(7x+10) = 13/12

We get x=2 years.

So difference in age 8x – 7x = 16 – 14 = 2 years.

Shortcut: We can use the below formula to find out value of ‘x’. Here new ratio difference = 13-12 = 1 and added number = 10 (years)

Cross multiplication difference = 96 – 91 = 5

X = (1 * 10)/5 = 2 years. : )

Q 3. The ratio between the ages of Prahlad and Ramavtar is 3:5 and difference between their ages after 4 years will be 10 years. What is the present age of Prahlad?

Explanation:

Generally people starts assuming the present age as x and then adding +4 to get ages after 4 years and later solve it by making equations. But do you know that will consume a lot of you time and we all know time is the key to crack any exam.

So here by basic concept no. 5, as the age difference between you and your friend is let’s suppose 6 years. And after 10 or 15 years this will be same as 6 years.

Hence the ration of their ages is 3:5

It mean actual age will be 3x and 5x.

Now the difference between their age will be 3x-5x = 10 (given)

So we get x = 5 years.

Age of Prahlad = 3x = 3 * 5 = 15 years.

Q 4. Ganesh is 24 years younger than his Father Bholenath. 3 years ago, Ganesh was 1/5 as old as his father was. What is Ganesh’s present age?

Explanation:

As per given 10 years, ratio between their age was Ganesh : Bholenath = 1x : 5x

Now Ganesh is 24 years younger than his father. It means their age difference will be 24 years.

Hence, 5x -1x = 24 years. => x= 6 years.

This age was 3 years ago so today Ganesh’s age will be 6 + 3 = 9 years.

Q 5. The total age of Ram and Shyam is 10 years more than that of total age of Shyam and Mohan. Mohan is how many years younger than Ram? (NABARD 2010)

Explanation:

R + S = S + M +10 => R = M + 10  => M = R -10

Hence Mohan is 10 years younger than Ram.

Have a look at the following questions:-

Ex. 1: The age of the father 3 years ago was 7 times the age of his son. At present, the father’s age is five times that of his son. What are the present ages of the father and the son?

Ex. 2: At present, the age of the father is five times the age of his son. Three years hence, the father’s age would be four times that of his son. Find the present ages of the father and the son.

Ex. 3: Three years earlier, the father was 7 times as old as his son. Three years hence, the father’s age would be four times of his son. What are the present ages of the father and the son?

Ex. 4: The sum of the ages of a mother and her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?

Ex. 5: The sum of the ages of a son and father is 56 yrs. After 4 yrs, the age of the father will be three times that of the son. What is the age of the son?

Ex.6: 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?

By the conventional method:-

Solution: 1.      Let the present age of son = x yrs

Then, the present age of father = 5xyr

3 years ago,

7(x – 3)= 5x – 3

Or, 7x – 21 =5x – 3

Or, 2x =18

x = 9 yrs

Therefore, son’s age = 9 years

Father’s age = 45 years

Solution: 2.      Let the present age of son = x yrs

Then, the present age of father = 5x yrs

3 yrs hence,

4(x+3)= 5x+3

Or, 4x + 12=5x +3

x= 9yrs.

Therefore, son’s age = 9 yrs and father’s age = 45 yrs

Solution: 3.      Let the present age of son = x yrs and the present age of father = y yrs

3 yrs earlier, 7(x – 3) = y – 3   or, 7x – y =18………….(i)

3 yes hence, 4(x+3) = y +3

Or, 4x +12 = y + 3                   or, 4x – y = – 9 …………(ii)

Solving (1) & (2) we get, x = 9 yrs & y =45 yrs

Solution: 4.      Let the age of the daughter be x yrs.

Then, the age of the mother is (50x – x)yrs

5 yrs ago, 7(x – 5) = 50 – x – 5

Or, 8x = 50 – 5 +35 = 80

x =10

Therefore, daughter’s age = 10 yrs and mother’s age = 40yrs

Solution: 5.      Let the age of the son be x yrs.

Then, the age of the father is (56 – x) yrs.

After 4 yrs, 3(x+4) = 56 – x +4

Or, 4x =56 +4 – 12 = 48

x = 12 yrs

Thus, son’s age = 12 yrs.

Solutions: 6.

Father            :           Son

Present age =        6                 :               1

After 5 yrs =           7                :               2

Son’s age = Father’s age = Other Method:-

Solution: 1.

Son’s age = =9 yrs

and father’s age = 9 × 5 = 45 yrs.

Undoubtably you get confused with the above method, but it is very easy to understand and remember. See the following form of question.

Question: t1 yrs earlier the father’s age was x times that of his son. At present the father’s age is y times that of his son. What are the present ages of the son and the father?

Formula Solution 2: Son’s age = = 9yrs  and father’s age = 9 × 5 =45 yrs

To make more clear, see the following form:

Questions: The present age of the father is y times the age of his son. t2 yrs hence, the father’s age become z times the age of his son. What are the present ages of the father and his son?

Formula Solutions.3:

Son’s age = = 9 yrs

To make the above formula clear, see the following form of question.

Questions: t1 yrs earlier, the age of the father was x times the age of his son. t2 yrs hence, the age of the father becomes z times the age of his son. What are the present ages of the son and the father?

Formula Solutions. 4:

Daughter ‘s age =  Thus, daughter’s age = 10 yrs and mother’s age = 40 yrs

Solutions. 5:

Son’s age =  Note : Do you get the similarities between the above two direct methods? They differ only in sign in the numerator. When the question deals with ‘ago’, a +ve sign exixts and when it deals with ‘after’, a –ve sign exists in the numerator.

Solutions. 6:    Then what formula comes?

Father                :                  Son

Present age =                  x                     :                     y

After T yrs=                     a                     :                     b

Then, Son’s age = And, Father’s age = Note:

1. While evaluating the difference of cross-product, always take +ve sign.

2. Both the above direct formulas look similar. The only difference you can find is in the denominators. But it has been simplified as “difference of cross-products” to make it easier to remember. So, with the help of one formula only you can solve both the question.

3. We suggest you to go-through both the methods and choose the better of the two.

We hope that the post would have cleared all your doubts related to the topic.

# Practice Set on Ages

• Four years ago the ratio of ages of A &B was 3 : 5 and five year hence the ratio will become 6:8. Find the present age of A?
A) 15yrs
B) 13yrs
C) 16yrs
D) 17yrs
E) 18yrs

Option A
Solution:
.                    A…….B

4yr ago         3……..5
Present        +3       +3
5yr after       6………8
So total 9 years
So 3 = 9
1 = 3
A’s age 4yrs ago = 9
A’s present age = 9+4 = 13

• Six year ago the ratio of ages of A & B was 1:3 and after six year the ratio becomes 2:3. Find the sum of present ages of A & B.
A) 24
B) 26
C) 28
D) 30

Option C
Solution:

.                    A…….B
6yr ago          1……..3
Present        +1       +0
6yr after       2………3
First of all we have to make same difference. So their difference will be multiplied with each other.
.                    A…….B
.                    1……..3
.                  +3       +3
.                   4………6
Now difference is same… 3 = 12
So 1 = 4
Present ages of A and B are 4+6= 10, 12+6= 18
Sum = 10+18 = 28

• The present ratio of ages of A & B is 11:12 and the ratio of ages of A’s 2yr back and B’s 6yr after is 2:3. Find age of A 6yr after?
A) 28yr
B) 30yr
C) 26yr
D) 36yr

Option A
Solution:

A/B = 11/12 ……….(1)
(A-2)/(B+6) = 2/3………(2)
By solving above equation we will get A = 22
So age of A 6yr after = 22+6 =28yr

• The average of 20 students class is 21. If the age of teacher is included then average increase by 2yr. Find age of teacher?
A) 60yr
B) 63yr
C) 66yr
D) 61yr

Option B
Solution:

If the age of teacher is 21 then average remains unchanged but due to increase by 2yr, it means teacher gave 2yr to everyone( 20+1) =21
21 + (21*2)
21+ 42= 63 yr

• Sita’s present age is 1(2/5) times of her age at the time of marriage. She married 10yr ago. Now she has a son whose age is 1 more than 1/5th of her age at the time of marriage. Find the age of son?
A) 3yr
B) 4yr
C) 5yr
D) 6yr

Option D
Solution:

Sita’s present age                Sita’s marriage age
7                                              5
+2
2 = 10
1= 5
5 = 25 yr
Now Sita’s son age is 1 more than 1/5th of her marriage time age.
1 + 25/5 = 6yr

• The ratio of father and son’s age is 7:4. The product of their ages is 2800. The ratio of their ages after 2yr will be ?
A) 7:12
B) 12:7
C) 3:5
D) 5:3

Option B
Solution:

Sol : let their age is 7x and 4x
Product = 28x² = 2800
x² =100
x = 10
Their ages = 70 : 40
2yrs after = 72 42
12 : 7

• The sum of the ages of father and son is 45yrs. Five years ago the product of their ages was 4 times the father’s age at that time the present ages of father & son are ?
A) 39,6
B) 35,10
C) 36,9
D) 40,10

Option C
Solution:

F + S = 45
5yr ago F + S = 35
A.T.Q = F * S = 4* F
S = 4yr
F = 31yr
Present age = 31+5 =36yr
4+5= 9 yr

• The ratio between the ages of father & son at present is 7:3. 4yr hence the ratio between son & his mother will be 1:2. Find the ratio of the present ages of father & mother?
A) 3:4
B) 5:4
C) 4:3
D) Can’t determined
E) None of these

Option D
Solution:

Let age of father & son …. 7x, 3x
4yr hence, son’s age = 3x+4
Ratio of ages of son & mother … 3x+4 : M = 1:2
M = 6x+8
F + M = 7x : 6x+4
We can’t find value of x. so ans is D.

• Three years ago the father was 7times as old as his son. Three year hence the father’s age would be 4times that of his son. Find present ages of father and son?
A) 25yr
B) 35yr
C) 45yr
D) 55yr

Option C
Solution:

.                   F  :  S
3yr ago         7  :  1.. …………..(1)
Present        -3    +0
3yrs after     4  :  1 …….……..(2)
We have to Make difference same.
Equation (1) * 3 equation (2) * 6
.     F………..S
.     21…….. 3
.     24……..6
Now difference 24-21 =3, 6-3 = 3 is same.
3 = 6
1 = 2
21 = 42
Present age =42+3 = 45 yr

• Mikesh was thrice as old as ajay 20 yrs back. How old is ajay today, if mikesh will be 50 yrs old 10 year hence?
A) 20yr
B) 30yr
C) 40yr
D) 50yr

Option B
Solution:

Mikesh’s present age =50-10 = 40yr
20 yrs back from now mikesh age = 20yr
Ajay is half = 10yr
Now ajay age = 10+20 =30yr.

• Ratio of present age of A and B is 7 : 9 and ratio of ages of A 5 years back and age of B 5 years later is 3:5. Find the present age of B.
A) 35 years
B) 45 years
C) 30 years
D) 50 years
E) 40 years

Option B
Solution
:

A/B=7/9
(A-5)/(B+5)=3/5
solve both and get A=35 and B=45

• 5 years ago the ratio of ages of A and B are 5:7 and 10 years hence from now ratio will become 4:5. Find the average of present age of A and B.
A) 30 years
B) 40 years
C) 35 years
D) 45 years
E) None of these

Option C
Solution
:

—————————–A ———— B
5 years ago ————- 5 ———-  7
10 years hence ——–  4 ———–5
Difference =      ——– (-1)——– (-2)
to make these two difference equal multiply the second equation with (7-5)=2
So we get
—————————–A ———— B
5 years ago ————- 5  ———-  7
10 years hence ——–  8 ———–10
Difference =      ——– (+3)——– (+3)
3=15 years (5 ago + 10 hence)
1=5 years
=> 5 = 25 years (5 years ago of A)
=>7=35 years (5 years ago of B)
Hence A=25+5=30
B=35+5=40 years
Avg=70/2=35

• The present age of a son is 40% of his father age. And the age of his mother is 220% of his age. The average age of three members is 38. Find the present age of mother.
A) 50 years
B) 22 years
C) 10 years
D) 44 years
E) None of these

Option D
Solution
:

Son= 40% of father.
F_S=5:2
Mother=220% of son=11/5
M_S=11:5
make F:M:S =25:22:10
avg=(25+22+10)/3=19
19=38
1=2
=>22=44

• Rama got married 8 years ago. Her present age is 1 (1/3) times of her age at the time of marriage. She has a son who is one eighth of her present age. Then find the age of her son.
A) 4 years
B) 3 years
C) 2 years
D) 5 years
E) None of these

Option A
Solution
:

1 (1/3)=4/3
Ratio of present age of Rama and her age at time of marriage=4:3 ——– difference =1
1=8 years
4=32
age of son=32/8=4 years

• A says to B “I am thrice as old as you are when I was as old as you were”. If age of B is 20 years find the age of A
A) 60 years
B) 30 years
C) 45 years
D) 36 years
E) None of these

Option B
Solution
:

A                B
3x              y
y                x
3x-y = y-x (difference is same)
4x=2y
x/y=1/2
2=20
1=10
3x=30

• The fathers age is four times as much as the sum of the age of his three children but 6 years hence his age will be thrice as the sum of their age. The present age of father is?
A) 60 years
B) 54 years
C) 42 years
D) 48 years
E) None of these

Option D
Solution
:

Let sum of children age=x ; hence father =4x
(4x+6)/x+6 = 3/1
x=12;
father=48

• In a class of 20 students the average of all the students is 18 years. If the age of their teacher is added then the average becomes 19 years. Find the age of teacher after 5 year.
A) 44 years
B) 39 years
C) 43 years
D) 38 years
E) None of these

Option A
Solution
:

Let age of teacher=x
(total age)/ total people=19
360+x/21=19
x=39
hence age after 5 years=44

• In a family there are 5 brothers in a gap of 2 years. If therir average age is 22 find the sum of eldest and youngest brother.
A) 42 years
B) 40 years
C) 38 years
D) 44 years
E) None of these

Option D
Solution
:

44
difference is same, hence 22 i.e is average is the age of middle son i.e
18,20,22,24,26 : age of 5 son
18+26=44

• Four years ago the ratio of ages of A and B is 3:5. After four years from now the ratio will be 5:7. Then find the ratio of their present age.
A) 5:7
B) 5:3
C) 2:3
D) 7:5
E) None of these

Option C
Solution
:

.                               A                       B
4 years ago    =        3                        5
4 years after  =        5                        7
Difference     =        2                        2
2=8 (4 ago + 4 hence)
1=4
present age A= 3*4 + 4=16
B=5*4 +4=24
16/24=2:3

• The average age of a couple at the time of their marriage was 22. Two years after the marriage their child was born. Now he is 4 years old. Find the average age of their present age.
A) 24 years
B) 22 years
C) 18 years
D) 20 years
E) None of these

Option D
Solution
:

Sum of couples age at time of marriage=2*22=44
when son was born, total age=44+2+2=48
After 4 years total age=48+4+4+4=60
avg=60/3=20

• The present age of Sumit is 1/8th of his father. After 4 years, the father’s age will be twice the age of Raman. If Raman celebrated his 6th birthday eight years ago, what is Sumit’s present age?
A) 4
B) 6
C) 5
D) 8
E) None of these

Option A
Solution:
Present ratio Sumit : Father is 1 : 8……………. (1)

4 years after, Father : Raman is 2 : 1………………..(2)
Raman’s 6th birthday was 8 years ago, so after 4 years he will be 18 years old
Put in equation (2), Raman = 18, Father = 36
So present age of father = 32
So of Sumit is 32/8 = 4 years

• Sita’s present age is five times of her daughter’s age and 1/3rd of her father’s age. If the average age of all the three is 28 years, then find the difference between Sita’s daughter’s age and her father’s age.
A) 50
B) 40
C) 56
D) 55
E) 62

Option C
Solution:
Sita : Daughter = 5 : 1

Sita : Father = 1: 3 or 5 : 15
Total age of 3 = 1 + 5 + 15 = 21
So average = 21/3 = 7
7…….28
1……..4
Sita’s daughter = 4
So her father’s = 60
Difference = 56 years

• Sheetal’s age at the time of her marriage was 4/5th of her present age. If she married 6 years ago and now she has a son who is 1/10th of her present age, then find the age of her son 5 years hence.
A) 3
B) 8
C) 9
D) 10
E) 12

Option D
Solution:
4/5 * 6 = 24/30

24 => at the time of marriage
30 years => now
Son = 1/10 of present age = 1/10 * 30 = 3 years
5 years hence = 3+5 = 8 years

• Ram is 6 years elder then his brother and 5 years younger than her sister Sheena. When Sheena was born, her father’s age was 24 and when Ram’s brother was born his mother’s age was 29. Find the difference between ages of Ram’s father and his mother.
A) 10
B) 8
C) 6
D) Cannot be determined
E) None of these

Option C
Solution:
Bother=x

Ram=x+6
Sheena=x+11
Father=x+11+24=x+35
Mother=x+29
Difference=x+35 –(x+29)=6 years

• When a couple was married, their average age was 22 years. When their first child was born, the average age of all the three became16 years. When their second child was born, the average of all 4 became 15 years. Find the average age of couple at the time when their second child was born.
A) 20
B) 28
C) 30
D) 32
E) 25

Option B
Solution:

At the time of marriage total age of couple=44

when 1st child is born total age of three=16*3=48
Difference=48-44=4 years (Child is of 0 years hence this is the sum of age incrase of couple)
When second child is born sum of age=4*15=60 years
=> increase of 12 years after first child, means age of husband, wife and first child increased by 4 years each. SO increase in husband and wife total age = 8 years
total increase =4+8=12
total age=44+12=56; average=56/2=28 years

• Five years ago, the ratio of ages of A and B was 5 : 3 and five years hence from now, the ratio will become 7 : 5. Find the average of their present ages.
A) 15
B) 18
C) 21
D) 25
E) 24

Option D
Solution:

———————A———–B
5 years ago—–5————-3
…………………—7————–5
In both case increase of 2 years 7-5=2 and 5-3=2
hence this increase of 2 years is for 10 years
=>1=5
hence A=5*5+5=30
B=3*5+5=20
Average=25

• Four years ago, the ratio of ages of Vishal and Devansh was 3 : 5. Four years from now, the respective ratio will become 2 : 3. What is the ratio of age of Vishal 4 years ago and Devansh’s present age?
A) 4 : 5
B) 1 : 2
C) 6 : 11
D) 3 : 4
E) 9 : 13

Option C
Solution:
—————————–V——————–D

4 years ago ————–3———————-5    ——-(eq 1)
4 years hence————2———————–3 ——- (eq 2)
Difference of V= 3-2=1; Difference of D= 5-3=2
to make this difference equal multiply eq 2, by 2 we get
—————————–V——————–D
4 years ago ————–3———————-5    ——-(eq 1)
4 years hence————4———————–6 ——- (eq 2)
difference = 1 in both case
This is for 8 years =>1= 8 years
V=3*8=24 (4 years ago)
D=5*8=40 (4 years ago)
ratio =24/44=6:11

• The average age of 10 men increased by 1 when two men of age 25 and 27 years are replaced by 2 other men. Find the average age of new men.
A) 31
B) 30
C) 26
D) 33
E) 28

Option A
Solution:
Sum of age of leaving person=52

total increase of of age=10*1=10 years
increased total age due to addition of two men=52+10=62; Avg=31
• The average age of a group of 20 men is 22 years. If two men whose age are 24 and 31 years respectively join the group, the average age of new group increase or decrease by
A) No increment , no decrement
B) increase by 0.5 year
C) decrease by 0.5 year
D) increase by 1 year
E) decrease by 1 year

Option B
Solution:
When 2 new people join if the sum of their age is 44 then the average will not change, but the sum of age of new people is 55 i.e increase of 11

hence avg increases by 11/22=0.5 years.

• The ratio of present age of Tiya and Piya is 3 : 5 and the ratio of ages of Tiya 5 years ago and Piya 5 years hence is 1 : 3. Find the present age of Piya.
A) 10
B) 25
C) 15
D) 30
E) 31

Option B
Solution:
T/P=3/5 ——- (i)
T-5/P+5 =1/3 ———- (ii)
Solve and get
T=15 years
P= 25 years

• Four times the difference in ages of C and A is one more than the age if B. Percentage of A’s age to C’s age is 75%. If ratio of B’s age 5 years hence to C’s age 1 year ago is 4 : 3. Find the average of ages A and C.
A) 20
B) 19
C) 12
D) 14
E) 8

Option D
Solution:

4 (C-A) = B + 1
A/C * 100 = 75
(B+5)/(C-1) = 4/3
Solve
A = 12, C = 16

• 10 years ago daughter’s age was two-fifth of her mother’s age that time. While 10 years hence her age will be three-fifth of her mother’s age then. Find the difference in the ages of the two.
A) 24
B) 19
C) 26
D) 38
E) 16

Option A
Solution:

(x-10) = 2/5 (y-10)
(x+10) = 3/5 (y+10)
Solve, x = 26 and y = 50

• B is as more younger than C as he is elder than A. Ratio of ages of A to C is 5 : 9. If B’s age after 10 years will be 24, find the average of all of their present ages.
A) 15
B) 16
C) 14
D) 22
E) 19

Option C
Solution:

B’s present age = 24-10 = 14
So C’ age = 14+x
And A’ age = 14-x
(14+x)/(14-x) = 9/5
Solve, x = 4
So average age = (10+14+18)/3 = 14 years

• Kaira is 4 years younger to his brother. Her father was 30 years old when her sister was born while her mother was was 30 years old when she was born. If her sister was 4 years old when their brother was born, find the age of her father when her mother was born.
A) 11
B) 12
C) 4
D) 10
E) 8

Option E
Solution:

When Kaira was born:
Mother was 30.
She is 4 years younger to her brother, so brother was 4 years old.
Sister was 4 years old when brother was born, so sister is 4 years elder to brother, so sister was 8 years old.
Father was 30 when sister was born, so father is 30 years elder to sister, so father was 30+8 = 38 years old.
Now when Kaira was born, mother was 30 and father was 38
So difference in their ages is 8 years. So when mother was born, father was 8.

• 6 years ago, three times the age of B was 2 more than the age if A that time. 6 years hence, twice age of B will be equal to A’s age that time. Find the total of their ages.
A) 48
B) 66
C) 56
D) 65
E) 60

Option B
Solution:

3 * (B-6) = 2 + (A-6)
2 * (B+6) = A + 6
Solve, A = 46, B = 20

• If 6 years are subtracted from the present age of Babita and the remainder is divided by 18, then the present age of her granddaughter Geeta is obtained. If Geeta is 2 years younger to Sita whose age is 5 years, then what is Babita’s present age?
A) 77
B) 65
C) 84
D) 43
E) 79

Option A
Solution:

Geeta’s age = (5-2) = 3 years
Let age of Babita = x years
So (x-6)/18 = 3
Solve, x = 60

• A’s age is twice C’ age. Ratio of age of B 2 years hence to age of C 2 years ago is 5 : 2. C is 14 years younger than D. Difference in ages of D and A is 4 years. Find the average of their ages.
A) 36
B) 25
C) 27
D) 13
E) 18

Option E
Solution:

A = 2C
(B+2)/(C-2) = 5/2
C = D – 14
D – A = 4
Solve, A = 20, B = 18, C = 10, D = 24

• When the couple was married the average of their ages was 25 years. When their first child was born, the average age of family became 18 years. When their second child was born, the average age of the family became 15 years. Find the average age of the couple now.
A) 31
B) 27
C) 28
D) 29
E) 30

Option D
Solution:

Sum of ages of couple = 25*2 = 50
When 1st child born, total age of 3 = 18*3 = 54 years
At this time the child’s age was 0, so age of father and mother would have increased by same. So increased by 2 years each. So 50 +2 + 2 = 54
Now when 2nd child born, total age of 4 = 15*4 = 60
So this time second child’s age = 0 and age of father, mother and first child would have increased by same. So increased by 2 each such that 54 + 2+2+2 = 60
So now this time (after 4 years from age 50), total age of couple is 50+4+4 = 58
So average = 29 years

• Ratio of age of A to B is 3 : 2 and that of A to C is 1 : 2. Difference in ages of B and C is 24 years. Find the average of their present ages.
A) 24
B) 22
C) 14
D) 26
E) 31

Option B
Solution:

B/A = 2/3 and A/C = 1/2
So B : A : C = 2*1 : 3*1 : 3*2 = 2 : 3 : 6
So 6x – 2x = 24, 4x = 24, x = 6
So total of their present ages = (2+3+6)*6. So average = (2+3+6)*6 / 3 = 22 years

• Ratio of ages of A 5 years hence to B’s age 3 years ago is 5 : 3. Also ratio of ages of A 4 years ago to B’s age 2 years hence is 4 : 5. Find the age of the elder.
A) 15
B) 18
C) 21
D) 20
E) 24

Option D
Solution:

(A+5)/(B-3) = 5/3
(A-4)/(B+2) = 4/5
Solve A = 20, B = 18