AGES

Problems based on ages are frequently asked In all exams. Actually, it is a very easy topic. First of all you should carefully read the question and form linear equations based on that and then solve those equations to find the age.

TYPE- I

1.

Midhun's age after 10 years will be 4 times his age 8 years back. What is the present age of Midhun
Let the present age be x 
After 10 yrs => x  10 = 4(x - 8) 
x  10 = 4x- 32
3x = 42 
x = 14
.'.The present age of Midhun is 14 yrs.

2.

Raji's age is 3 times that of Simi at present. After 15 years, Raji's age will be 2 times that of Simi. Then what is the present age of Raji
Let the present age of Simi be x.
Then, Raji's age = 3x 
After 15 years =>3x  15 = 2(x  15) 
3x  15 = 2x  30 
x =15
.'.Raji's age = 3 x 15 = 45 years

3.

After 15 years, Satheesh will be 4 times old as he was 15 years ago. What is his present age?
Let the present age of Satheesh be x 
After 15 yrs => x  15 = 4(x - 15) 
x 15 = 4x-60
3x = 75
x = 25
.'.Present age of Satheesh is 25 yrs

4.

18 years ago, Praveen was 3 times as
old as Prajeesh. Now Praveen is twice old as Prajeesh. What is the sum of their present ages?
Let the present age of Prajeesh be x 
Then, Praveen's present age = 2x 
18 yrs ago => 2x - 18 = 3(x-18)
2x - 18 = 3x - 54
x = 36
.'.Praveen's age = 2 x 36 = 72 
.'. Sum of their ages = 36  72 = 108

5.

The age of father 10 years ago was thrice the age of his daughter. 10 years hence father's age will be twice that of his daughter. What is the present age of father?
Let the present age of daughter be x 10 yrs ago => f - 10 = 3(x- 10)
10 yrs hence => f  10 = 3(x  10)
10 yrs hence=>f-10=2(x10)
f-10=3x-30
-f-10=-2x-20/-20=x-50
Solving => -20=x-50
x=30
Now, f-10 = (3x30)-30 
f-10 = 90-30 
f = 70
.'.The present age of father is 70 yrs

TYPE -II

1.

The ratio of the ages of a father and son is 3 : 1. If the sum of their ages is 64, find the age of son.
Let the age of son be x
Then, father's age = 3x 
Given, 3x  x = 64 
4x = 64 
x =16 
.'.The age of son is 16 yrs.

2.

The present ages of 3 persons are in the proportion 3:5:7. 6 years ago, sum of their ages was 57. Find their present ages.
Given, a : b : c = 3 : 5 : 7 
Let a = 3x, b = 5x and c = 7x 
6 yrs ago =>
(3x - 6)  (5x - 6)  (7x - 6) = 57
15X-18 = 57
x =5
.'.Their present ages are 15 yrs, 25 yrs and 35 yrs.

3.

The ages of Anand and Pratap are in the ratio 3 :5. The difference of their ages is 8. Find the age of Anand.
Given, A : P = 3 : 5 
Let A = 3x and P = 5x 
5x - 3x = 8 
2x = 8 
x =4
.'.Age of Anand = 3 x 4 = 12 yrs

4.

The sum of the ages of 3 friends 10 years hence is 120. Their present ages are in the proportion 2:3: 4. Find their ages at present.
Given, a : b : c = 2 : 3 : 4 
Let a = 2x, b = 3x and c = 4x 
After 10 yrs =>
(2x10)(3x10)(4x10)
=120
9x30=120
x=10
.'.Their present ages are 20 yrs, 30 yrs and 40 yrs.

5.

The ratio of father's age to son's age is 4: 1. The product of their ages is 196. What will be the ratio of their ages after 5 years
Let the age of son be x 
Then, father's age = 4x 
Given, 4x*x = 196 
4X2 = 196 
x2 =49 
x=7
.'. Present ages are 28 yrs and 7 yrs 
.'.Ratio of their ages after 5 yrs 
= (28  5) : (7  5)
= 33:12 
= 11:4

6.

The ages of Rakhi and Kumar are in the ratio 3:5. After 9 years, the ratio of their ages will be 3:4. Find the present age of Rakhi.
R: K =3:5 
Let R = 3x and K = 5
After 9 yrs =>3x9/5x9 = 3/4
4(3x  9) = 3(5x  9)
12x  36 = 15x27
3x =9 
x =3
.'.Present age of Rakhi is 3 x 3 = 9 yrs

TYPE - III

1.

The sum of ages of 9 persons is 630. After 5 years interval, they met together. Then, what is the average of their ages.
After 5 years =>
Sum of the ages of 9 persons
= 630  (9 x 5)
= 630  45 = 675 
.'.Average=675/9=75

2.

The average age of P and Q was 21 years, 4 years ago. The average became 25 when R joined them. How old is R now.
(P  Q)'s total present age =
(2 x 21  4  4) = 50
(P  Q  R)'s total present age = 25 x 3 = 75
.'. R's age = 75 - 50 = 25 yrs

3.

The average age of 50 students in a class is 25 years. The average remained the same even after the age of teacher was induded. Find the age of teacher.
Average age of 50 students is 25
Total age = 25 x 50 = 1250
1250  x=2 51
1250 x = 1275
x = 25
.'.Age of teacher is 25 yrs