**Problems On Ages**

**1. The Ratio of Ages of Mona and Sona is 4:5. Twelve Years hence, their ages will be in the ratio of 5:6. What will be Sona's age after 6 years ?**

**Sol:**Let their present ages be 4x & 6x

Then (4x + 12)/(5x + 12) = 5/6 or x=12

Sona's age after 6 years = (5x +6) = 66 years

**2.Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What their present ages ?**

**Sol :**Let son's age 8 years ago be x years

Then Ramu's age at that time = 4x years

Son's age after 8 years = (x +8) + 8 = (x + 16) years

Ramu's age after 8 years = (4x + 8) + 8 = (4x + 16) years

2(x + 16) = 4x + 16 or x=8

Son's present age = (x + 8) = 16 years

Ramu's present age= (4x + 8) = 40 years

**3. A man is four times as old as his son. Five years ago, the man was nine times as old his son was at that time. What is the present age of a man ?**

**Sol :**Let son's age = x, then man's age =4x.

9(x - 5) = (4x-5) or x=8.

Man's present age = (4x + 7) = 35 years

**4. The sum of ages of Aruna and her mother is 49 years. Also, 7 years ago, the mothers age was 4 times Aruna's age. Find the present age of Aruna's mother**.

**Sol :**Let Aruna's age 7 years ago be x.

Mother's age 7 years ago = 4x

(x + 7) + (4x + 7) =49 or x=7

Mother's present age = (4x + 7) = 35 years

**5. The ages of A and B differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.**

**Sol :**Let A's age = x & B's age = (x + 16)

3(x - 6) = (x + 16 - 6) or x=14

A's age = 14 years & B's age = 30 years.

y = 5 - 2 ; y = 3 x – 18 (3) = 6 ; X – 54 = 6 ; X = 6 + 54

= 384 = -----------(2)

x – 1 = 4 (y – 1) put y = a in (1) we get x value as 33 33 : 9 ;

**6.**The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is:

a. 5 : 2

**b. 7 : 3**c. 9 : 2 d. 13 : 4**Answer with Explanation:**Let the father age be x years

Let the son’s age be y years

Given : 10 years ago, father age was thrice son age

X – 10 = 3 (y – 10)

x- 3y = -30 +10

x-3y = - 20 ---------------- (1)

Given : 10 years after, father age was twice son age

X + 10 = 2 (y + 10)

X – 2y = 10 -----------------(2)

To find : Ratio of present age (x : y = ?)

To get y value subtract (2) from (1)

Y = 30 ; substitute this value in (1) we will get x value

X = 70

70 : 30

**7 : 3**

**7.**The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?

a. 31 b. 36

**c. 51**d. None of these**Answer with Explanation:**

36 = 14

37 = 15 (teacher’s age included then average increased by one ; ie =15)

To find :

Teacher’s age:

(37 – 36) 15 = (15-14) (36)

15 + 36

**51 years**

8. If 6 years are subtracted from the present age of Gulzar and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Mahesh whose age is 5 years, then what is the present age of Gulzar?

**Answer : 60**

**Answer with Explanation:**Let the present age of Gulzar be x years

Let the present age of Anup be y years

Let the present age of Mahesh be z years

Given: = y

X – 6 = 18y

X – 18y = 6

Given : Anup is 2 years younger to Mahesh

Y = z – 2

Given : Mahesh age is 5 years

Z = 5

X = 60

To find : Present age of gulzar

**X = 60 years**

9. The average age of five members of a family is 21 years. If the age of the grandfather be included, the average is increased by 9 years. The age of the grandfather is :

**Answer : 75**

**Answer with Explanation:**

Given :

Number of members Average

5 21

5 +1 21 + 9

5 21

6 30

To find : Grand father’s age

Grand father age = (6-5) (30) + (30-21) (5)

= 30 + 45

**= 75**

10. The average age of a n adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The originals strength of the class was:

**Answer : 12**

**Mean =****Answer with Explanation:**

Let be the sum of the ages of n adults

Let be the sum of the ages of 12 students

Given : =

**40 =**

40 n = --------------------(1)

**32 =**

**32 x 12 =**

(1) + (2) + = 40N + 384 ---------------------(3)

From the given statement,

(3) = decreasing the age of the class by 4 years

40 n + 384 = (n +2) 36 40n – 36n = 432 – 384

**N = 12**

11. One year ago, a father was four times as old as his son. In 6 years time his age exceeds twice his son’s age by 9 years. The ratio of their present ages is :

**Answer : 11:3**

**Answer with Explanation:**

Given : Let the present age of father be x years

Let the present age of son be y years

X -1 = 4y – 4

X – 4y = -3 -----------------(1)

Given : In 6 years time, father age exceeds twice son by 9 years

X + 6 = 2 (y +6) +9)

X – 2y = 21 – 6

X – 2y = 15 ---------------(2)

(1) – (2) -2y = -15

Y = 9

To find: Ratio of present age of father and son

X : y = ?

**The ratio of present age of father and son = 11:3**

12. Ramlal is four times as old as his son. Four years hence, the sum of their ages will be 43 years. The present age of the son is :

**Answer : 7**

**Answer with Explanation:**

Let the present age of Ramlal be x years

Let the present age of son be y years

Given : x = 4y x – 4y = 0 ---------------(1)

Given : x +4 + y + 4 = 43

X + y = 35 ------------------------ (2)

To find : Present age of son (ie) y = ?

(1) – (2)

- 5y = - 35

Y = 7

**Answer : Present age of son is 7 years**

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