Question 1

The age of the father 4 years ago was 8 times the age of his son. At present, the father's age is 4 times that of his son. Find the present age of son.

Accepted Answer

Question 2

A man is 3 years older than his wife and four times as old as his son. If the son becomes 15 years old after 3 years, then what is the present age of the wife?

Accepted Answer

Suppose age of son = P years Age of the man = 4P years Age of man's wife = 4P – 3 years According to the question, After 3 years, age of son + 3 years = 15 P + 3 = 15 ∴ P = 15 – 3 = 12 years Now, age of wife = 4P – 3 years age of wife = 4 × 12 – 3 years age of wife = 48 – 3 years age of wife = 45 years

Question 3

The age of Dr. Pandey is four times the age of his son. After 10 years, the age of Dr. Pandey will be twice the age of his son. The present age of Dr. Pandey's son is :

Accepted Answer

Question 4

Five years ago, Mayank's mother was three times as old as Mayank. After five years she will be twice as old as Mayank. The present age of Mayank is :

Accepted Answer

Method (1) Let us assume the present age of Mayank is X and his mother age is Y. Five years ago, Mayank's age = X - 5 Five years ago, Mayank's mother age = Y - 5 According to question, Five years ago, Mayank's mother was three times as old as Mayank. Y - 5 = 3 (X - 5) ⇒ Y - 5 = 3X - 15 ⇒ 3X - Y = 15 - 5 ⇒ 3X - Y = 10................(1) Again According to question, After five years, Mayank's age = X + 5 After five years , Mayank's mother age = Y + 5 After five years she will be twice as old as Mayank. Y + 5 = 2 ( X + 5 ) ⇒ Y + 5 = 2X + 10 ⇒ Y - 2X = 10 - 5 ⇒ Y - 2X = 5 ....................(2) Add the equation (1) and (2), we will get 3X - Y + Y - 2X = 10 + 5 X = 15 Put the vale of X in equation (2), We will get Y - 2 x 15 = 5 Y + 30 + 5 = 35 years Mayank' Present Age is 15 years and mother age is 35 year. Method 2 Let us assume the present age of Mayank be P, then the 5 years before Mayank's age = P - 5 According to Question Age of his mother before 5 years = 3 x (P - 5 ) Present age of his mother = 3 x (P - 5 ) + 5 After 5 Years Mayank's age = P + 5 After 5 Years Mother' age = 3 x (P - 5 ) + 5 + 5 Now again according to question, After five years she will be twice as old as Mayank, then 3 x (P - 5 ) + 5 + 5 = 2 (P + 5) ⇒ 3P - 5 = 2P + 10 ⇒ 3P - 2P = 10 + 5 ⇒ P = 15 Mayank's present Age is 15 years.

Question 5

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. What are their present ages?

Accepted Answer

Lt us assume the present age of father is P and son age is Q. According to question, P + Q = 45.................. (1) Five years ago, the father age = P - 5 Five years ago, the son age = Q - 5 According to question, Five years ago, the product of their ages was four times the father's age at that time. (P - 5) (Q - 5) = 4 (P - 5) PQ - 5P - 5Q + 25 = 4P - 20 PQ - 5P - 5Q + 25 - 4P + 20 = 0 ⇒ PQ - 9P - 5Q + 45 = 0 ⇒ P(Q - 9) - 5(Q - 9) = 0 ⇒ (Q - 9) (P - 5) = 0 ⇒ (Q - 9) = 0 or (P - 5) = 0 ⇒ Q = 9 or P = 5 Put the vale of Q in equation (1), we will get. if Q = 9 then P = 45 - 9 = 36 which is matched our answer. If P = 5 then Q = 45 - 5 = 40 years which is not match our answer. Method 2 Let the present ages of father and his son be x and (45 - x) years respectively; then according to question, (x - 5) (45 - x - 5) = 4 (45 - x -5) ⇒ x - 5 = 4 ⇒ x = 9 Now, Father's age = 45 - x = 45 - 9 = 36 years

Question 6

The difference between the present ages of Arun and Barun is 14 years. 7 years ago the ratio of their ages was 5 : 7 respectively. The present age of Barun is :

Accepted Answer

Let the present ages of Arun and Barun are x and x +14 years respectively; then According to question, 7 years ago the ratio of their ages was 5 : 7 (x - 7)/(x + 14 - 7) = 5/7 ⇒ (x - 7)7 = 5(x+14 - 7) ⇒ 7x - 49 = 5x + 35 ⇒ 2x = 84 ∴ x = 42 Hence, age of Barun = 42 + 14 = 56 years

Question 7

The ratio between the ages of Ram and Mohan is 4 : 5 and that between Mohan and Anil is 5 : 6. If sum of the ages of three be 90 years, what is the age of Mohan?

Accepted Answer

Here, ratio of ages of Ram, Mohan and Anil = 4 : 5: 6 Let their present ages be 4x, 5x and 6x years respectively. then 4x + 5x + 6x = 90 ⇒ 15x = 90 ∴ x = 6 Hence, age of Mohan = 5 x 6 = 30 years

Question 8

Ten years ago, the age of Divya was half of the age of Namrata. If the ratio of present ages of both is 3 : 4, the sum of their present ages is:

Accepted Answer

Let the present age of Divya and Namrata are 3x and 4x years respectively; then According to question, Ten years ago, Age of Divya = 3x - 10 Ten years ago, Age of Namrata = 4x - 10 Now According to question, Ten years ago, the age of Divya was half of the age of Namrata 3x - 10 = (4x - 10)/2 ⇒ 6x - 20 = 4x - 10 ⇒ 2x =10 ∴ x = 5 Hence, sum of their ages = 3x + 4x = 7x =7 x 5 = 35 years

Question 9

The present ages of three persons are in the ratio of 4 : 7: 9. Eight years ago, the sum of their ages was 56. What are their present ages in years?

Accepted Answer

Let the present age of three persons are 4x, 7x and 9x years respectively. Eight years ago, Ages of three person were 4x - 8, 7x - 8, 9x - 8 years. According to question, 4x - 8 + 7x - 8 + 9x - 8 = 56 ⇒ 20x - 24 = 54 ⇒ 20x = 80 ∴ x = 4 Hence, their present ages are 4 x 4 = 16 years, 7 x 4 = 28 years, 9 x 4 = 36 years respectively .

Question 10

The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1 : 1. The ratio between A's age 4 years hence and B's age 4 year ago is:

Accepted Answer

Let the present ages of A and B are 5x and 3x years respectively. Then A's age 4 years ago = 5x - 4 B's age 4 years hence = 3x + 4 According to question, The ratio between A's age 4 years ago and B's age 4 years hence is 1 : 1 (5x - 4)/(3x + 4) = 1 : 1 = 1 ⇒ 5x - 4 = 3x + 4 ⇒ 2x = 8 ∴ x = 4 present ages of A and B are 20 and 12 years. The ratio between A's age 4 years hence and B's age 4 year ago is: Hence, required ratio = (20 + 4) : (12 - 4) = 24 : 8 = 3: 1

Question 11

The ratio of ages of a man and his wife is 4 : 3. After 4 years, this ratio will be 9 : 7 If at the time of marriage the ratio was 5 : 3, then how many years ago were they married?

Accepted Answer

Let the present ages of the man and his wife are 4x and 3x years respectively; then After 4 years ages of man and his wife will be 4x + 4 and 3x + 4 years. According to question, After 4 years, this ratio of their ages will be 9 : 7, (4x + 4)/ (3x + 4) = 9/7 ⇒ (4x + 4)7 = 9(3x + 4) ⇒ 28x + 28 = 27x + 36 ∴ x = 8 Hence, their present ages are 4 x 8 = 32 years and 3 x 8 = 24 years If t years ago they were married, then (32 - t) /(24 - t) = 5/3 ⇒ (32 - t)3 = 5(24 - t) ⇒ 96 -3t = 120 - 5t ⇒ 2t = 24 ∴ t = 12 years

Question 12

A is two years older than B, who is twice old as old as C. If the sum of the ages of A, B and C be 27, then the age of B in years is:

Accepted Answer

Let us assume the age of B be P years then age of A will be P + 2 and age of C will be P/2 years. Then according to question, P + 2 + P + P/2 = 27 ⇒ P + P + P/2 = 27 - 2 ⇒ ( 2P + 2P + P)/2 = 25 ⇒ 5P = 25 x 2 &there; P = 50/5 = 10 years Age of B will be 10 years.

Question 13

Sudha's grandfather was 8 time older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Sudha's age to that of her grandfather?

Accepted Answer

Let us assume 16 years ago, the age of Sudha and her grandfather were x and 8x years respectively; then Present age of Sudha = x + 16 Present age of her grandfather = 8x + 16 After 8 years age of sudha from now = x + 16 + 8 After 8 years age of grandfather from now = 8x + 16 + 8 now according to question, He would be 3 times of her age 8 years from now. 3(x + 16 + 8) = 8x + 16 + 8 ⇒ 3x + 72 = 8x + 24 ⇒ 5x = 48 ∴ x = 48/5 Eight years ago , sudha age = x + 16 - 8 = x + 8 Eight years ago , grandfather age = 8x + 16 - 8 = 8x + 8 Hence, required ratio = (x + 8) / (8x + 8 ) Put the vale of x , we will get ⇒ required ratio = (48/5 + 8) / ( 8 x 45/5 + 8) ⇒ required ratio = ((48 + 40)/5) / ( (8 x 45 + 40)/5) ⇒ required ratio = (88/5) / ( 400/5) ⇒ required ratio = 88 / 400 ⇒ required ratio = 11 : 50

Question 14

The sum of ages of A and B is 12 years more than the sum of ages of B and C. Then C is how many years younger than A?

Accepted Answer

Let us assume the A age is P , B age is Q and C age is R years. Sum of the age of A and B age is P + Q years and B and C ages is Q + R Years. According to question, The sum of ages of A and B is 12 years more than the sum of ages of B and C Here, (P + Q) = (Q + R) + 12 ⇒ (P + Q) - (Q + R) = 12 ⇒ P - R = 12 ∴ P = R + 12 Hance, C is 12 years younger than A.

Question 15

Ram got married 8 years ago. His present age is 6/5 times his age at the time of marriage. Ram's sister was 10 years younger to him at the time of his marriage. What is the present age of Ram's sister?

Accepted Answer

Let the present age of Ram be x years; then 8 years ago Ram age = x - 8 According to question, His present age is 6/5 times his age at the time of marriage. x =( x - 8) 6/5 ⇒ 5x = 6x - 48 ∴ x = 48 Age of Ram at the time of his marriage = 48 - 8 = 40 According to question, Ram's sister was 10 years younger to him at the time of his marriage Hence, Ram's sister age at the time of his marriage = 40 - 10 = 30 years. So Present age of Ram's Sister = 30 + 8 = 38

Question 16

Q is as much younger than R as he is older than T. If sum of the ages of R and T is 50 years, what is the difference between R and Q's age?

Accepted Answer

Let us assume Q age is Q years , R age is R years and T age is T years. According to question, Q is as much younger than R as he is older than T Age of Q - T = R - Q ∴ Q = (R + T)/2 If sum of the ages of R and T is 50 years. Hence, age of Q = 50/2 = 25 years Here, absolute value of age of R is not known. So the difference between R and Q's age cannot be determined. Hence, data is inadequate.

Question 17

The sum of the ages of 5 children born at the interval of 3 years each is 50 years . The age of youngest child is:

Accepted Answer

Let us assume the age of youngest child be P years. Then according to question, The age of 5 children born after every 3 years will be P , P + 3, P + 6, P + 9, P + 12. Now as we know from the given question The sum of the ages of 5 children born at the interval of 3 years each is 50 years P + (P + 3) + (P + 6) + (P + 9) + (P + 12) = 50 ⇒ 5P + 30 = 50 ⇒ 5P = 20 ∴ P = 4 years

Question 18

A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now. Five years ago the age of son was :

Accepted Answer

Let us assume the present age of child is P years. Then according to question, I was as old as you are at present at the time of your birth. Father's age were at the time of son's birth = P years Again According to question Present age of father = 38 Father's age were at the time of son's birth + Present age of Son = 38 P + P = 38 2P = 38 ∴ P = 19 years Hence, 5 years ago the age of son was 19 - 5 = 14 years

Question 19

The mother is five times older then her son. After 4 years, the sum of their ages will be 44 years. What is the present age of the son?

Accepted Answer

Let us assume the present ages of son be P then mother's age will be 5P years. After 4 years, Son' age = P + 4 After 4 years, Mother' age = 5P + 4 According to question, 5P + 4 + P + 4 = 44 ⇒ 6P = 36 ∴ P = 6 years

Question 20

A person said : Take my age three years hence, multiply it by 3 and then subtract 3 times my age three years ago and hence everybody will know how old I am ". The age of person in years is:

Accepted Answer

Let us assume the present age of the person be P years. 3 years hence the age of person = P + 3 3 years ago the age of person = P - 3 According to question, Take my age three years hence, multiply it by 3 and then subtract 3 times my age three years ago, = 3(P + 3) - 3(P - 3) = 3P + 9 - 3P + 9 = 18 years Hence, age of the person = 18 years

Problems on Ages Questions