Problems On Ages Tricks & Tips
How to solve Problems based on Ages Part-1
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)
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TYPE 1:
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?
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?
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?
Let the son’s present age be X,
Then,(38-X)=X
2X=38
X=19 years
TYPE 2:
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?
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?
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
TYPE 1:
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?
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?
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
TYPE 2:
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?
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?
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?
New Ratio Difference=13-12=1
Added number =10 years.
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
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 ?
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.
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.
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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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
- 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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
- The present age of Sumit is 1/8^{th} of his father. After 4 years, the father’s age will be twice the age of Raman. If Raman celebrated his 6^{th} birthday eight years ago, what is Sumit’s present age?
A) 4
B) 6
C) 5
D) 8
E) None of these - Sita’s present age is five times of her daughter’s age and 1/3^{rd} 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 - Sheetal’s age at the time of her marriage was 4/5^{th} of her present age. If she married 6 years ago and now she has a son who is 1/10^{th} of her present age, then find the age of her son 5 years hence.
A) 3
B) 8
C) 9
D) 10
E) 12 - 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 - 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 - 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 - 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 - 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 - 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 - 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
- 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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
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