PROBLEMS ON AGES1) The ratio between the current age of A and B is 6:7. If B is 4 years old than A. What will be the ratio of the ages of A and B after 4 years?A) 3 : 1 B) 4 : 5 C) Data inadequateD) 4 : 3 E) None of these

If A’s age and B’s age will be 6A years and 7A years correspondinglyThen, 7A – 6A = 4, A = 4Needed ratio = (6A + 4) : (7A + 4) = 28 : 32 = 7 : 8

2) The Avg age of a class of 22 subject areas in 21 years. The avg increased by one when the lecturer’s age also involved. What is the age of the Lecturer?A) 41 B) 43 C) 44 D) 40

Average * Subject Areas = Total AgeSo => 21 years x 22 numbers = 462 years … (1)=> 22 years x 23 numbers = 506 years … (2)Therefore Lecturer’s age = Eqn(2) – Eqn(1) = 506 – 462 = 44 Years.

3) Right now, the ratio between the ages of Karthikh and Prasath is 4:3. After 6 years, Karthikh’s age will be 26 years. What is the age of Prasath right now?A) 19 years B) 21 years C) 25 years D) 15 years

If the current ages of Karthikh and Prasath be 4A years and 3A years correspondingly.Then, 4A + 6 = 26, 4A = 20, A = 5Prasath’s age = 3A = 15 years.

4) A father is two times as old as his daughter. 2 decades ago, the age of the father was 12 times the age of the daughter. The current age of the father isA) 22 B) 32 C) 44 D) 45

Let daughter’s age = A., Then father’s age = 2A12 (A – 20) = (2A – 20), 10A = 220, A = 22Father’s current age = 44 years.

5) 1 decad ago, Naresh was 3 times as old as Abdul was but 10 years hence, he will be just two times as old. Find Naresh’s current ageA) 70 years B) 60 years C) 80 years D) 66 years

Condition : Naresh’s current age is A years and Abdul’s current age is B years.Then, based on the first condition,

A – 10 = 3[B - 10] or, A – 3B = -20 ..(1)Here, Naresh’s age after 10 years =(A + 10) yearsAbdul’s age after 10 years = (B + 10) , (A+10) = 2(B+10) or, A – 2B = 10 ..(2)Solving Eqn(1) & Eqn(2), we will get A = 70 and B = 30Naresh’s age = 70 years and Abdul’s age = 30 years.

6) Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.3 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas’s current age in years?A) 14 B) 42 C) 24 D) cannot be determined E) None of these

If current ages of Rahim and Thomas be 5A years and 4A years correspondinglyThen, 5A + 3 = 114A + 3 = 99(5A + 3)=11(4A + 3)A = 6Thomas’s current age = 4A= 24 years.

7) A father is Quadrice as old as his daughter today. After 20 years, he would be only two times as old. At the time of daughter’s birth, how much old the father be?A) 37 C) 31 B) 35 D) 30

If the ages of daughter and father today by ‘A’ and ’4A’ years correspondingly.4A + 20 = 2 (A+20)A = 10 years => 4A = 40 years.At the time of daughter’s birth, father’s Age40 – 10 = 30 years old

8) The overall ages of Kumar, Hathim and Rahul is 93 years. 1 decade ago, the ratio of their ages was 2 : 3 : 4. What is the current age of Rahul?A) 24 years B) 38 years C) 28 years D) 44 years

If the ages of Kumar, Hathim and Rahul 1 decade ago be 2A, 3A and 4A years correspondinglyThen, (2A + 10) + (3A + 10) + (4A + 10) = 939A = 93-309A = 63A = 7Rahul’s current age = (4A + 10)= 38 years.

9) Amith was 3 times as old as Harsh 6 years back. Amith will be 5/3 times as old as Harsh 6 years hence. How much old is Harsh today?A) 12 years B) 21 years C) 11 years D) 22 years

Let Harsh’s age 6 years back = AThen, Amith’s age 6 years back = 32.Then 5/3 (A + 6 + 6) = (3A + 6 + 6)5(A + 12) = 3 (3A + 12)4A = 24A = 6Harsh’s age today = (A + 6) years= 12 years.

10) The ages of Smirthi and Samantha vary by 16 years, Six years ago, Deepika’s age was three times as that of Smirthi’s, find their current ages.A) 10 years, 28 years B) 11 years, 28 years C) 14 years, 30 years D) 16 years, 34 years

Let Smirthi’s age = A yearsSo, Deepika’s age = (A + 16) yearsAlso, 3(A – 6) = A + 16 – 6 or, A = 14Smirthi’s age = 14 yearsand, Deepika’s age = 14 + 16= 30 years

11) Sachin is 40 years old and Vijay is 60 years old. How many decades ago was the proportion of their ages 3 : 5?A) 37 years B) 27 years C) 20 years D) 10 years

If the ratio was 3 : 5, ‘A’ years ago.Then, 7A – 6A = 4A = 4Then, {( 40 – A)/(60 – A)}= (3/5)5 (40 – A) = 3(60 – A)2A = 20A = 10

12)  15 years hence, Karthikh will be just Quadrice as old as he was 15 years ago, How old is Karthikh at now? [ Quadrice = 4 Times ]A) 35 B) 25 C) 20 D) 30

Let the current age of Karthikh = A yearsThen, A+15 = 4(A – 15)Therefore A = 25

13) The current ages of 3 individuals are in the ratio 4:7:9.  0.8 decades ago, the sum of their ages was 56. Find their current ages in yearsA) 16, 28, 36B) 18, 30, 38C) 20, 32, 46D) None of these

Let their current ages are 4A, 7A and 9A years correspondingly.Then, (4A – 8) + (7A – 8) + (9A – 8) = 5620A = 80A = 4Their current ages are16 years, 28 years and 36 years correspondingly.

14)  At present, the ratio between the ages of Akbar and Denial is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present?

Let the present ages of Akbar and Danial be 4x years and 3x years respectively. Then, 4x + 6 =26 ⇔ 4x = 20 ⇔ x = 5.∴ Deepak’s age = 3x =15 years.

15) 1 Decade ago, Karthikh’s mother was quadrice older than her son. After one decade, the mother will be two times older than her son. The current age of Karthikh is?[Decade = 10 Years;  quadrice= 4 times]A) 8 years B) 12 years C) 20 years D) 23 years

Let Karthikh’s age 10 years ago be A yearHis mother’s age 1 decade ago = 4A(4A + 10) + 10 = 2 (A + 10 +10)2A = 20 or A =10Current age of Karthikh = (A + 10)= 20 years

16) A person’s age is 125% of what it was one decade ago, but 83(1/3)% of what it will be after one decade. What is his current age? [1 decade = 10 years]A) 35 years B) 40 years C) 50 years D) 55 years

Let, current age is A years.Then, 125% of (A – 10) = Aand, 83(1/3)% of (A + 10) = ATherefore 125% of (A-10) = 83(1/3)% of (A+10)or, (5/4) (A – 10) =(5/6)(A+10)or, (5/4)A -(5/6)A = (50/6)+(50/4)

or, (5A/12)= (250/12) or,A=50 years.17) One decade ago, X was half of Y in age. If the proportion of their current ages is 3:4, what will be the overall of their current ages?A) 10 years B) 20 years C) 25 years D) None of these

Let the ages of X and Y 1 decade ago be A and 2A years correspondingly.Then, [ (A +10)/2A+10) ] = (3/4)4 (A – 10) = 3(2A – 10)2A = 10A = 5Therefore,Sum of theircurrent ages = (A + 10) + (2A + 10) = (3A + 20)= 35 years.

18) Father’s age today is three times as his daughter’s. After 10 years it would be just twice. What is the daughter’s age today?A) 9 B) 10 C) 12 D) 15

Let, today’s age of the daughter = ‘A’ years.Mom’s age today = 3A yearsAfter 1 decade,3A + 10 = 29A + 10=> A = 10 years

19) A person is 24 years elder than his daughter. In 2 years, person’s age will be 2 times the age of his daughter. Then the current age of the daughter is:A) 14 years C) 20 years B) 18 years D) 22 years

Let, daughter’s current age is A years. Then, person’s current age = (A +24) years.(A + 24) + 2 = 2 (A + 2)A + 26 = 2A + 4A = 22

20) 0.2 decades ago a person was 6 times as old as his daughter, After 18 years, he will be two times as old as his daughter. Then their current ages are,[0.2 decades = 2 years]A) 7 B) 9 C) 11 D) None of theseAns: None of these.

21) A man’s current age is (2/5) of the age of his father. After 8 years, he will be (1/2) of the age of his father. What is the age of father at now?

A) 50 years B) 40 years C) 33 years D) 43 yearsLet, father’s current age is A years.Then, Man’s current age =[ (2/5)A ]years.Therefore, [ (2/5)A + 8 ]= (1/2)(A + 8)2(2A + 40) = 5(A + 8)A = 40

22)  If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,A) 30 years B) 38 years C) 40 years D) 41 years

Let daughter’s age = A and mother’s age = BGiven:2A+B = 70 and,A+2B = 95Solving B, we will get B = 40.

23) The avg age of class of 20 students in 20 years. If the lecturer’s age is added to the avg, increases by one. What is the age of the lecturer?A) 30 B) 40 C) 31 D) 41Average x Number = Total Years20 x 20  = 400  …(1)21 x 21  = 441 …(2)Lecturer’s age =Eqn (2) -Eqn (1)= 441 – 400= 41 years

24) The age of mother one decade age was three times the age of her daughter. 10 years hence, mother’s age will be two times that of her daughter. The proposition of their current ages is:A) 6 : 1 B) 7 : 3 C) 8 : 6 D) 10 : 5

Let, Ages of mother and daughter 1 decade ago was 3A and A years correspondinglyThen, (3A + 10) + 10 = 2 [(A + 10) + 10]3A + 20 = 2A + 40X = 20Needed Ratio = (3A + 10) : (A + 10)= 70 : 30= 7 : 3

25) If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now?

A) 40 B) 41 C) 36 D) 48

Raj’s age today = 17 decades,Hence, 5 decades back, he must be 12 years old.Rahim must be 36 years old, Because (3×12).5 years back Rahim must be 41 years old today. Because (36+5).

26)  3 years ago, the avg age of a family of 5 individuals was 17. A kid have been born the avg age of family is an exact today? What is the age of the kid?A) 2 years B) 3 years C) 4 years D) 5 year

Current age of 5 individuals is,=5 x 17 + 3 x 5 = 100 yearsAlso, current ages of 5 persons + Age of the kid= 6 x 17 = 102 yearsTherefore, Age of the Kid = 102 – 100 = 2 years.

27)  0.1 decates ago, Vijaya was quadrice as old as her daughter Simran. 0.6 decades hence, Vijaya’s age will beat her daughter’s age by 0.9 decades. The proportion of the current ages of Vijaya and Simran is :[ 0.1 Decates =1 Year; quadrice = 4 times]A) 8 : 1 B) 10 : 2 C) 11 : 4 D) 13 : 4

Let, Ages of Vijaya and Simran – 1 year ago was 4A and A years correspondingly.Then, [(4A + 1) + 6] – [(A + 1) + 6] = 93A = 9X = 3Needed Ratio = (4A + 1) : (A + 1)= 13 : 4

28)  The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be[1 Decade = 10 years]A) 4 : 3 B) 12 : 11 C) 7 : 4 D) 6 : 5

Let, Maala’s age = 4A and Kala’s age = 3AThen 4A + 3A = 28A = 4Maala’s age = 16 yearsand Kala’s age = 12 yearsProportion of their ages after 8 is = (16 + 8) : (12 + 8)= 24 : 20= 6 : 5

29)  The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X?A) 10 B) 12 C) Z is elder than X D) None of these

(X + Y) – (Y + Z) = 12X – Z = 12[Age in decades = 1.2]

30)  The proportion of X’s and Y’s ages is 4:5. If the difference between the current age of X and the age of Y 0.5 decades hence is 3, then what is the sum of current ages of X and Y?A) 72 years B) 62 years C) 52 years D) 82 years

We simplified the most of steps because lack of font prolem.X = 32 yearsand, Y = (5/4) x 32 = 40 yearsTherefore X + Y = 40 + 32 = 72 years.

31. Rabert’s age after 15 years will be 5 times his age 5 years back. What is the present age of Rabert?  

Let Rabert’s present age be x years. Then,Rabert’s age after 15 years = (x + 15) years.Rabert’s age 5 years back = (x - 5) years.∴ x + 15 = 5 (x - 5) ⇔ x + 15 = 5x - 25⇔ 4x = 40 ⇔ x = 10.Hence, Rabert’ present age = 10 years.

32. The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father.

Let the son’s present age be x years. Then father’s present age = (3x + 3) years.∴ (3x + 3 + 3) = 2 (x + 3) + 10 ⇔ 3x + 6 = 2x + 16 ⇔ x = 10.Hence, father’s present age = (3x + 3) = (3x + 3) = (3 * 10 + 3) years = 33 years.

33. The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages. Let the age of the younger person be x years. Then, age of the elder person = (x + 16) years. ∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10

⇔ 2x = 28 ⇔ x = 14 Hence, their present ages are 14 years and 30 years.

34. Peter got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Peter’s sister was 10 years younger to him at the time of his marriage. The age of Peer’s sister is:

Let Peter’s present age be x years. Then, his age at the time of marriage = (x - 8) years.∴ x = 6/5 (x - 8) ⇔ 5x = 6x - 48 ⇔ x = 48.Peter’s sister’s age at the time of his marriage = (x - 8) - 10= (x - 18) = 30 years.∴ Peter’s sister’s present age = (30 + 8) years = 38 years.

35. The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the some of the ages of his sons. The father’s present age is :

Let the sum of present ages of the two sons be x years.Then, faher’s present age = 3x years.∴ (3x + 5) = 2 (x + 10) ⇔ 3x + 5 = 2x + 20 ⇔ x = 15.Hence, father’s present age = 45 years.

36. The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?

(A + B) - (B + C) = 12 ⇔ A - C = 12.

37. The sum of the present ages of a father and his son is 60 years. Six year ago, father’s age was five times the age of the son. After 6 years, son’s age will be.

Let the present age of son and father be x and (60 - x) years respectively.Then, (60 - x) - 6 = 5 (x - 6) ⇔ 6x = 84 ⇔ x = 14.∴ Son’s age after 6 years = (x + 6) = 20 years.

38. One year age, Promila was four times as old as her daughter Jenilia. Six years hence, Promila’s age will exceed her daughter’s age by 9 years. The ratio of the present ages of

Promila and her daughter is :

Let the ages of Promila and Jenilia 1 year ago be 4x and x years respectively.Then, [(4x + 1) + 6] - [(x + 1) + 6] = 9 ⇔ 3x = 9 ⇔ x = 3.∴ Required ratio = (4x + 1) : (x + 1) = 13:4.

39. Four years ago, the father’s age was three times the age of his son. The total of the ages of the father and the son after four years, will be 64 years. What is the father’s age at present?

Let the ages of father and son 4 years ago be 3x and x years respectively.Then, [(3x + 4) + 4] + [(x + 4) + 4] = 64 ⇔ 4x = 48 ⇔ x =12.∴ Father’s present age = 3x = 36 years.

40. Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :

Let the present ages of the father and son be 2x and x years respectivelyThen, (2x - 18) = 3 (x - 18) ⇔ x = 36.∴ Required sum = (2x + x) = 3x = 108 years.

41. 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 the son is:

Let the son’s present age be x years. Then, man’s present age = (x + 24) years.∴ (x + 24) + 2 = 2(x + 2) ⇔ x + 26 = 2x + 4 ⇔ x = 22.

42. The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)

Let thier present ages be 4x, 7x and 9x years respectively.Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 ⇔ 20x = 80 ⇔ x = 4.∴ Their present ages are 16 years, 28 years and 36 years respectively.

44. Three years ago, the average age of a family of 5 members was 17. A baby having been born the average age of the family is the same today? What is the age of the child?

Present age of 5 members = 5 x 17 + 3 x 5 = 100 yearsAlso, present ages of 5 members + Age of the baby = 6 x 17 = 102 yearsAge of the baby = 102 – 100 = 2 years