Question 1

The ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1:3. What are the ages of A and B?

Accepted Answer

Let us assume the ages of A and B be 3x and 11x years; then After 3 years the ages of A and B will be 3x + 3 and 11x + 3. According to question, After 3 years the ratio of the ages becomes 1: 3, (3x + 3)/(11x + 3) = 1/3 ⇒ 3 (3x + 3) = 1 (11x + 3) ⇒ 9x + 9 = 11x + 3 ⇒ 2x = 6 ∴ x = 3 Hence, their present age, 3x = 3 x 3 = 9 years; 11x = 11 x 3 =33 years

Question 2

In 10 years A will be twice as old as B was 10 years ago. If A is now 9 years older than B, what is the present age of B?

Accepted Answer

Method 1 Let the present age of B and A be x and ( x + 9 ) years; then, Age of B and A after 10 years will be x + 10 and x + 9 + 10; According to question, In 10 years A will be twice as old as B was 10 years ago 2(x - 10) = x + 9 + 10 2x - 20 = x + 19 ⇒ 2x - x = 19 + 20 ∴ x = 39 years Method 2 Let us assume the present age of B and A be x and y years. According to question, A is now 9 years older than B, y = x + 9...........(1) Again according to question, In 10 years A will be twice as old as B was 10 years ago y + 10 = 2( x - 10)................. (2) now put the value of y from equation (1) in above equation (2) x + 9 +10 = 2x - 20 ⇒ 2x - x = 19 + 20 ⇒ x = 39 years So Present age of B = 39 years.

Question 3

Radha get married 6 years ago. Today her age is 1 1/ 4 times her age at the time of marriage. Her son's age is 1/10 times her age. Her son's age is :

Accepted Answer

Let us assume the present age of Radha be Y years; then Before 6 years Radha's age will be Y - 6 years. According to question, Today her age is 11/4 times her age at the time of marriage, 5/4 ( Y - 6 ) = Y ( Since 11/4 = 5/4 ) ⇒ 5Y - 30 = 4Y ∴ Y = 30 years Hence, her son's age = 30 x 1/10 =3 years

Question 4

Two years ago, the ratio of Ram's and Mohan's age was 3 : 2 and at present 7 : 5. What are their present ages?

Accepted Answer

The ratio of Ram's and Mohan's present age is 7 : 5. Let us assume the present ages of Ram and Mohan are 7Y and 5Y years. 2 Years ago the age of Ram and Mohan will be 7Y - 2 and 5Y - 2 years. According to question, Two years ago, the ratio of Ram's and Mohan's age was 3 : 2, then (7Y -2)/(5Y - 2) = 3/2 ⇒ (7Y -2) x 2 = 3 x (5Y - 2) ⇒ 14Y - 4 = 15Y - 6 ∴ Y = 2 Hence, their present ages = 7 x 2 = 14 years and 5 x 2 = 10 year

Question 5

One year ago, the ratio of Yamini and Gamini's was 6 : 7 respectively. Four year hence, the ratio would become 7 : 8. Find the age of Gamini?

Accepted Answer

Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively; then (6P + 5)/(7P + 5) = 7/8 ⇒ (6P + 5) x 8 = 7 x (7P + 5) ⇒ 48P + 40 = 49P + 35 ∴ P = 5 Hence, present ago of Gamini = 7P + 1 = 7 x 5 + 1 = 36 years

Question 6

The ages of Surabhi and Neerja are in the ratio of 6 : 7 respectively. After 6 years the ratio of their ages will be 15 : 17. Find the age of Neerja.

Accepted Answer

Let the present ages of Surabhi and Neerja are 6x and 7x years respectively. According to question, (6x + 6)/(7x + 6) = 15/17 ⇒ (6x + 6)x17 = 15x(7x + 6) ⇒ 102x + 102 = 105x + 90 ⇒ 3x = 12 ∴ x = 4 Hence, present ages of Neerja = 7 x 4 = 28 years

Question 7

The average age of a woman and her daughter is 42 years. The ratio of their ages is 2 : 1 respectively. Find the daughter's age.

Accepted Answer

Let us assume the present ages of woman and her daughter be 2x and x years respectively ; then According to question, The average age of a woman and her daughter is 42 years (2x + x)/2 = 42 ⇒ 3x = 84 ∴ x = 28 Hence, present age of her daughter = 28 years

Question 8

The ages of A and B are in the ratio of 11 : 13 respectively. After 7 years the ratio of their ages will be 20 : 23. What is the difference in years between their ages?

Accepted Answer

Let the present ages of A and B are 11x and 13x years respectively; then According to question, After 7 years the ratio of their ages will be 20 : 23. (11x + 7 ) / (13x + 7) = 20/23 ⇒ (11x + 7 ) 23 = 20 (13x + 7) ⇒ 253x + 161 = 260x + 140 ⇒ 7x = 21 ∴ x = 3 Hence, difference of their ages = 13x - 11x = 2x = 2 x 3 = 6 years

Question 9

The average age of A, B and C is 25 years. The ratio of their age is 3 : 5 : 7. What is the age of A?

Accepted Answer

Let the present ages of A, B and C are 3x, 5x and 7x years respectively; then According to question, 3x + 5x + 7x = 3 x 25 ⇒ 15x = 75 ∴ x = 5 Hence, age of A = 3x = 3 x 5 = 15 years

Question 10

Three years ago, the average age of a family of five members was 17 years. A baby having been born, the average age of the family is the same as what was three years ago. The present age of the baby is:

Accepted Answer

Let us assume the present age of baby Y year. According to question, Three years ago, the average age of a family of 5 members was 17 years. The present Total age of the family of 5 member = 5 x 17 + 5 x 3 =100 ..........(1) Again according to question, The average age of the family is the same as what was three years ago. The present average age of family of 6 member= 17 Total present age of family of 6 member / 6 = 17 (Total present age of family of 5 member + present age of baby)/6 = 17 100 + Y = 17 x 6 Y = 17 x 6 - 100 = 102 - 100 = 2 years

Question 11

Present age of Rahul is 5 years less than Ritu's present age. If 3 years ago Ritu's age was x years, which of the following represents Rahul's present age in years?

Accepted Answer

3 Years age Ritu's age was x years, then Ritu's present age = x + 3 years According to question, Present age of Rahul is 5 years less than Ritu's present age Hence, present age of Rahul = x + 3 - 5 = x - 2 years

Question 12

The present age of Sanyal is 3 times the present age of his son. Six years hence, the ratio of their ages will be 5 : 2 respectively. The present age of Sanyal is:

Accepted Answer

Let us assume the present age of son be x then his father present age will be 3x. According to question, Six years hence, the ratio of their ages will be 5 : 2 respectively (3x + 6)/(x+6) = 5/2 ⇒ (3x + 6)2 = 5(x+6) ⇒ 6x + 12 = 5x + 30 ∴ x = 18 Hence, age of Sanyal = 3 x 18 = 54 years

Question 13

The ratio of ages of Namrata and Divya is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 4 years will be:

Accepted Answer

Let the present ages of Namrata and Divya are 4x and 3x years respectively; then According to question, 4x + 3x = 28 ∴ x = 4 Hence, their present ages are 16 and 12 years. So required ratio = (16 +4) : (12 + 4) = 20 : 16 = 5 :4

Question 14

At present, the ratio between the ages of Gopal and Madhawa is 4 : 3. After 6 years, Gopal's age will be 26 years. The present age of Madhwa is:

Accepted Answer

Let the present age of Gopal and Madhawa are 4x and 3x years respectively; then According to question, 4x + 6 = 26 ⇒ 4x = 20 ∴ x = 5 Hence, present age of Madhawa = 3x = 3 x 5 = 15 years

Question 15

The sum of the ages of Ram, Shyam and Mohan is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. The present age of Mohan is:

Accepted Answer

Let us assume 10 years ago, ages of Ram, Shyam and Mohan were 2x, 3x and 4x years respectively. Present ages of Ram, Shyam and Mohan will be 2x + 10 , 3x + 10 and 4x + 10 years. According to question, 2x + 10 + 3x + 10 + 4x + 10 = 93 ⇒ 9x + 30 = 93 ⇒ 9x = 93 - 30 ⇒ 9x = 63 ⇒ x = 7 The present age of mohan = 4x + 10 = 4x7 + 10 = 38 years

Question 16

The age of Shyam is 1/3 rd that of his mother. He is 2 years older than his sister. The age of his sister be 8 years, what is the age of his mother?

Accepted Answer

Question 17

Ramu is 48 years old. Robin is 6 years junior to Ramu and 14 years senior to Rohit. Ramu has two children – Neethu and Vinu. Youngest sister of Rohit is Krishna and she is 15 years junior to him. So what is the age of Krishna?

Accepted Answer

According to question , Given :- Age of Ramu = 48 years Age of Robin = Age of Ramu - 6 years = 48 – 6 = 42 years Age of Rohit = Age of Robin - 14 years = 42 – 14 = 28 years Age of Krishna = Age of Rohit - 15 years = 28–15 =13 years Hence , Age of Krishna is 13 years .

Question 18

The average age of 30 students is 15 years. If the teacher's age is also included then the average age increases by 1 year. The age of the teacher is

Accepted Answer

According to question , The average age of 30 students = 15 years Total age of 30 students = 30 × 15 = 450 years Total age of 30 students and teacher = ( 15 + 1 ) × 31 = 496 years ∴ Age of teacher = Total age of 30 students and teacher - Total age of 30 students Age of teacher = ( 496 – 450 ) = 46 years

Question 19

A was born 5 years before B, B is 4 years older than C and 3 years younger to D. If A is now 17 years old, how old is D?

Accepted Answer

Here , Present age of A = 17 years Age of B = age of A - 5 years = 17 – 5 = 12 years Age of C = age of B – 4 years =12 – 4 = 8 years Age of D = Age of B + 3 years =12 + 3 = 15 years

Question 20

Ashok's mother was 3 times as old as Ashok 5 years ago. After 5 years she will be twice as old as Ashok. How old is Ashok today?

Accepted Answer

Suppose the present age of Ashok is P years and that of his mother is Q years. 5 years ago , 3 × ( age of Ashok - 5 ) = ( age of Ashok 's mother - 5 ) 3 ( P – 5 ) = ( Q – 5 ) ⇒ 3P – 15 = Q – 5 ⇒ 3P – Q = 10 ....(i) 5 years after, 2 × ( age of Ashok + 5 ) = ( age of Ashok 's mother + 5 ) 2 ( P + 5 ) = ( Q + 5 ) ⇒ 2P + 10 = Q + 5 ⇒ 2P – Q = – 5 ....(ii) From equations (i) and (ii) , we get P = 15 years Hence , the present age of Ashok is 15 years .

Problems on Ages Questions