Problem on Age( For All Competitive Exams)
📝Chapter 8: Problems On Age.
Written by: Elisa Lalrinngheta ( Zo Guide Founder)
@Copyright Reserved by the author
Bibliography: He zirlai Problem on Ages hi UPSC, SSC, Banking Railway leh Competitive Exam ah hian an zawt uar hle a. NCERT Zirlai leh testbook a problem thenkhat lak khawm ani bawk. Chhiar tu ten an hlawkpui ngei ka beisei.
✅Introduction:
Kum(Age) kaihhnawih zawhna te hi competitive exam-a arithmetic reasoning pawimawh tak an ni. Heng zawhna te hi a tlangpuiin linear equation hmangin mi pakhat emaw a aia tam emaw kum hrang hranga an upat zawng zawn chhuah a ni thin. A hnuaiah hian zawhna chi hrang hrang, formula pawimawh tak tak, leh chinfel dan tur te chu chipchiar takin a tarlan a ni.
📝 Key Concepts in Age Problems (Age Kaihhnawih Zawhnaa Thu Pawimawh Te):
1.Present Age (Tunlai Kum): Mi pakhat tunlai tak an upat zawng.
2.Past Age (Hman Kum): Mi pakhat kum engemaw zat liam taa an upat zawng.
✅Formula:
Past Age = Present Age - Number of years ago
3.Future Age (Nakina Kum): Mi pakhat kum engemaw zat lo la awmtura a upat zawng.
✅Formula:
Future Age = Present Age + Number of years after
4.Age Difference (kum Inthlauhna):
Mi pahnih upat zawng inthlauhna hi a danglam ngai lo.
Entirnan: Mary hi kum x lo ni ta se, a thiannu J.Rini hi kum 5 in a upa zawk a nih chuan, kum engemaw zat hnuah pawh an inthlauhna hi a la ngai reng ang.
Common Equations (Equation Hman Dan Tlangpui):
Mi pakhat present age (Tuna a kum ) chu 'x' anih chuan:
➡️Kum 'y' hnu lama a upat zawng = x+y years.
➡️Kum y liam taa upat zawng = x-y years.
Upat zawng ratio hi a:b in lo ngai ta ila,
✅Mary tuna a kum = a × multiplier ,
✅J.Rini present age= b× multiplier.
🌫️Common Types of Ages Problem ( Ages problem larzual chi hrang hrang te):
1. Based on Present Ages: Hetiang ang chi ah hi chuan , mi pakhat emaw a aia tam kum zat min lo pe thina, a tum ber chu kum bo te zawn emaw inzawmna siam emaw a ni.
✅Example 1: A is 5 years older than B. If A is 18 years old, find the present age of B.
Solution:
B's age 18-5 = 13 years
.. The correct answer is 13 years.
✅Example 2: The sum of the present age of 3 persons is 125 years. If the average age of two persons is 5 less than the present age of the 3rd person, then find the present age of the third person.
Solution:
Given: Sum of present ages of 3 persons say A, B and C = 125 years
Calculations: (A + B + C) = 125
➡️ (A + B) = (125 - C) _______(1)
And,
(A + B) / 2 = (C - 5) __________(given)
Now, form equations (1) substitute the value of A+ B in given Equations we get,( he tah hian equations 1 ah hian A+ B value kan nei tawh a chu chu given Equations tia ka chhinchiah ah hian dah luh mai tur ani e.)
125-C/2= C-5
( = sign a awm reng reng chuan 1/2=3 lo nei ta ila , 1= 2×3 ani a cross multiplication tihna ani chu.
Chuan '+' hi = leh lam ah a kan sawn chuan '-' ah a chang thin ang chutiang bawkin '-' hi a phei chuan
'+' ah a chang ang)
C value zawn chhuah kan tum ang, C awmna number reng reng kha hmun khatah dah vek rawh
Left hand side ah hi dah ta ila,
➡️ 125 - C= 2C - 10 ➡️ 2C+ C = 125+10
➡️ 3C= 130 ➡️ C= 135/3= 45
The present age of the third person is 45 years.
✅The correct answer is 45 years.
✅Example 3: Three times the present age of Renu is 11 years more than two times the present age of Manav, and three times the present age of Manav is 9 years less than four times the present age of Renu. The sum of the present ages (in years) of Renu and Manav is?
2.Kum kalta (past) leh Tunlai(present ) behchhan in : Heng zawhnaah te hian mi pakhat kum chu hun hnih (hlui leh tunlai) a khaikhin a ni.
3.Kum lo awm tura innghahna:
Heng harsatnate hian mi pakhat kum lo awm tur chu an kum tuna an nih mek emaw, an kum hmasa lama an nih tawh emaw nen khaikhin na a tel a ni.
Entirnan:
4.Kum Chawhrual( Ratio) Harsatna Te:
Heng harsatna te hian mi pahnih emaw a aia tam kum chawhrual tehkhin nan a hmang.
Entirnan: The ratio of the present ages of A and B is 3:2. After 5 years, the ratio will be 4:3. Find their present ages.
Solution: Let their present ages be 3x and 2x.
(3x+5)/ (2x+5)= 4:3 or 4/3
After 5 years:
Cross-multiply and solve for x.
You get x = 5, so A's age 15 years and B's age = 10 years.
5.Kum chhiar nan Sum (zawmkhawm) emaw Difference (Inthlauhna) hman:
Heng harsatnate hian mi pahnih emaw a aia tam kum zawmkhawm emaw Inthlauhna an pe a, kum mal te te in a zawt fo thin.( UPSC exam ah hian an uar)
✅Example : The sum of the present ages of a mother and her daughter is 40 years. After 10 years, the mother's age will be twice that of her daughter. Find their current ages.
Solution:
Let the daughter's current age be x years.
Mother's current age = 40 - x
After 10 years: (40 - x) + 10 = 2(x + 10)
Solving for x, you get the daughter's current age as 10 years and the mother's as 30 years.
The correct answer is 10 years and 30 years.
📝Other example:
6. Average Age Problems: These problems involve calculating the average age of a group of people.( Heng ang chi ah hian chuan mipui a group anga awm ho an zavaia ages lak khawm a chhut chhuah ani.)
✅Example : The average age of three siblings is 20 years. If the age of the eldest sibling is 25 years, what is the total age of the other two siblings?
Solution:
Total age of three siblings = 20 x 3 = 60 years
Age of the eldest sibling = 25 years
Total age of the other two = 60-25 = 35 years ..
The correct answer is 35 years.
Other Example:
______________Thank you________________
✅UPSC Old Question and Answers(2014-2024)
Q1. A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age in 51 years. What is the age of the son? [CSAT 2015]
(a) 7 years
(b) 5 years
(c) 4 years
(d) 3 years✅
Solution: Given that,
A father is nine times as old as his son and the mother is eight times as old as the son.
The sum of the father's and the mother's age in 51 years.
Now,
Let the age of Son be S
Age of father = 9S
Age of mother =8S
9S + 8S = 51
S = 3
Thus the age of the son is 3 years
Hence option (d) is correct
Q2. The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3: 2. However, each saves Rs. 6,000 per month. What is their total monthly income? [CSAT 2017]
(a) Rs. 28,000
(b) Rs. 42,000✅
(c) Rs. 56,000
(d) Rs. 84,000
Solution:
Given that,
The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3:2
Each saves Rs. 6,000 per month.
Now,
Let income be I and expenses be E
Income = 4I : 3I
Expenses = 3E : 2E
4I - 3E = 6000.....(i)
3I - 2E = 6000.....(ii)
Thus by solving the equation (i) and (ii)
I = E = 6000
Therefore, income of X = 4 x 6000 = 24000
Income of Y = 3 x 6000 = 18000
Total income = 24000 + 18000 = 42000
✅ Hence option (b) is correct
Q3. The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again? [CSAT 2017]
(a) 42
(b) 38✅
(c) 25
(d) 16
Solution:
Given that,
The age of Mr. X last year was the square of a number and it would be the cube of a number next year.
Now,
Assuming the age of last year which is a square can be 1, 4, 9, 16, 25, 36.....
After 2 years the age is cube
After 2 years age will be 3, 6, 11, 18, 27, 38....
Thus age last year was 25 and next year will be 27 and present age is 26
Again the age will be cube = 64
Difference 64 - 26 = 38
Thus it will take 38 years
➡️ Hence option (b) is correct
Q4. Ena was born 4 years after her parents’ marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?[CSAT 2019)
(a) 22 years
(b) 23 years✅
(c) 24 years
(d) 25 years
Solution:
Given that,
Ena was born 4 years after her parents’ marriage.
Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old.
Now,
Ena's age = 13
Mother's age = 24 + 13 = 37 years
Fathers age = 40
Then,
Ena's father age during marriage = 40 - (13 + 4) = 23 years
Hence option (b) is correct
Q5. In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth? [CSAT 2019]
(a) 1992
(b) 1994
(c) 1996✅
(d) 1998
Solution:
Given that,
In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera.
Now,
Let meera age in 2002 be A
Meenu age in 2002 = A/3
In 2010
Meera age = A + 8
Meenu age = (A/3) + 8
Also,
➡️(1/2) x (A + 8) = [(A/3) + 8]
➡️A/2 + 4 = A/3 + 8
➡️A/6 = 4
➡️A = 24
Meenu age = 24/3 = 8
Year of birth = 2002 - 8 = 1994
✅ Hence option (b) is correct
Q6. X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct? [CSAT 2021]
(a) 1 only
(b) 2 only✅
(c) Both 1 and 2
(d) Neither 1 nor 2
Solution:
Given that,
X said to Y, "At the time of your birth I was twice as old as you are at present."
The present age of X is 42 years
Now,
Let the age of Y be a years
Age of X = 42 - a
Also, Age of X = 2a
42 - a = 2a
a = 14 years
Present age of Y = 14 Years
1. 8 years ago, the age of X was five times the age of Y.
8 years ago age of Y = 14 - 8 = 6 years
Age of X = 42 - 8 = 34 years
Hence statement 1 is incorrect
2. After 14 years, the age of X would be two times the age of Y.
After 14 years age of Y = 14 + 14 = 28 years
Age of X = 42 + 14 = 56
X = 2Y
Hence statement 2 is correct.
Q7. A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages? [CSAT 2024]
(a) 30 years✅
(b) 32 years
(c) 34 years
(d) 36 years
Solution:
Given that,
Father age is equivalent to son's present age n years back
Fathers age is 4 times son's age n years back
Sum of fathers age and Sons age is 130 years
Now,
Let the present age of Father and son be F and S
F - n = S......(i)
F = 4 x (S - n).....(ii)
F + S = 130......(iii)
Solving equation (i) and (ii)
F = S + n
S + n = 4S - 4n
5n = 3S
n = 3S/5
So, F = 8S/5......(iv)
Putting the value of equation (iv) in (iii)
(8S/5) + S = 130
13S = 130 x 5
S = 50 years
Thus, F = 130 - 50 = 80 years
Difference between their ages = 80 - 50 = 30 years
Hence option (a) is correct
📝Mizoram Public Service Commission Old Questions Under Various Department:
Q1. Five years hence, the age of John will be thrice that of Linda. Five years ago, John's age was seven times that of Linda. Then their present ages respectively will [UDC 19-RD]
a) 40, 10✅
d) 30, 20
b) 30, 10
c) 40, 20
Solution:
Q2.The ratio of the ages of a man and his son is 7:2. After 5 years their ages will be in tha ratio 8:3. The present age of the man is [MCS 2021]
(a) 56 years
(b) 45 years
(c) 35 years✅
(d) 40 years
Solution:
Let the present age of the man be 7x years and the son be 2x years, where x is a constant.
After 5 years, the man's age will be (7x+5) years, and the son's age will be (2x+5) years.
Q3. A man's age is three times the sum of the ages of his two sons. After 5 years, his age will be twice the sum of the ages of his two sons. How old is the man now? [Asst 19]
Solution:
Q4. Ten years ago A was half of B's age. If ratio of their present ages is 3:4 then what is the total of their present ages? [Store keeper 19]
a) 30 years
b) 35 years
c) 8 years
d) 20 years
Solutions:
✅Banking old questions practice set:
1.Sachin is younger than Rohan by four years. If their ages are in the respective ratio of 7:9, how old is Sachin?
a).16 years
b).28 years
c).18 years
d).None of these
2.The ratio between the present ages of X and Y is 6: 7. If Y is four years older than X, what will be the ratio of the ages of X and Y after four years? (S.B.I.P.O. 1998)
(a)3:4
(b)3:5
(c)4:3
(d) None of these
3.The ratio between the present ages of and B is 5:7 respectively. If the difference between B’s present age and A’s age after six years is 2, what is the total of A’s and B’s present ages? (Bank P.O. 1999)
(a) 48 years
(b) 52 years
(c) 56 years
(d) None of these
4.At present, the ratio between the ages of Arundhati and Diksha is 4:3. After six years, Arundhati’s age will be 26 years. What is the age of Diksha at present?
(a) 12 years
(b) 15 years
(c) 19 ½ years
(d) 21 years
5.My sister is three years older than me. My mother was 28 years of age when my brother was born, while my father was 26 years of age when I was born. If my brother was four years of age when my sister was born, then what was the age of my mother and father respectively when my sister was born?
a).32yrs, 23 yrs
b).32yrs, 39 yrs
c).35 yrs, 29 yrs
d). 35 yrs, 33 yrs
✅Answers key:
1.D
2.D
3.A
4.B
5.A
📝Practice Questions set -5:
Q1. At present, A is younger than B by 8 years. If 4 years ago, their ages were in the ratio 1:2, then what is the present age of B (in years)?
a) 16
b) 18
c) 20
d) 24
Q2.Three years ago, the ratio of the age of father to that of his son was 8:3. After 4 years, their ages will be in the ratio 11:5. What is the present age (in years) of the father?
a) 45
b) 48
c) 51
d) 54
Question 3. The ratio of present ages of A and B is 7:8. After 6 years from now, the ratio of their ages will be 8:9. If C's present age is 10 years more than A, then the present age (in years) of C is:
a) 42
b) 48
c) 52
d) 58
Q4.Ratio of the present age of a mother to that of the daughter is 7:1. After 5 years the ratio will become 4:1. What is the difference (in years) in their present ages?
a) 25
b) 28
c) 30
d) 32
Q5.B is twice as old as A. C is twice as old as B. If the difference between ages of A and C is 12 years, find the age of B.
a) 6
b) 7
c) 8
d) 9
✅Answers key:
1. c
2.c
3.c
4.c
5.c
