Dear Reader,
Below are three age problems which involve equation solving.

Question 1

Rajarajan retired after serving in Indian army as Lt. Colonel. Rajarajan's age is 20 times that of number of daughters he has. Each of his daughters has as many daughters as they have sisters. If total number of grand daughters of Rajarajan is 1/3rd of the number of daughters, find the age of Rajaran.

a) 72 b) 90 c) 80 d) 70

Answer : c) 80

Solution I :

Let the number of daughters of Rajarajan be - x
No. of sisters each daughter has - (x-1)
No. of daughters for each daughter - (x-1)
Then total number of grand daughters - Number of daughters x Number of grand daughter per daughter = x (x - 1)

It is given that total number of grand daughters of Rajarajan is 1/3rd of the number of daughters.
Therefore x = 1/3 (x (x - 1))
Or x - 1 = 3 or x = 4.
It is given that Rajarajan's age is 20 times that of number of daughters.
Therefore, his age = 20 X 4 = 80.

Solution II : (short cut)
Actually there is a simpler short cut to this problem. Since it is given that Rajarajan's age is 20 times that of number of daughters , his age should be divisible by 20. Among the options given only 80 is divisible by 20. Hence it is the answer.

Question 2

There are three employees in a software company in different levels. They have put in different years of service in the company. Arul is as much younger than Babu as he is older than Siva. If the sum of the ages of Babu and Siva is 60 years, what is definitely the difference between Arul’s age and Babu’s age?

a) 1 year b) 2 years c) 30 years d) data inadequate.

Answer : d) data inadequate.

Solution :

Babu's age - Arul's age = Babu's age - Siva's age => Arul's age = Siva's age -> (1)
Also Babu's age + Siva's age = 60
From eq (1) we know Siva's age is equal to Arul's age. Then above equation becomes,
Babu's age + Arul's age = 60 . However, from this equation one cannot find the difference between Babu's age and Arul's age. Hence data is inadequate.

Question 3

Manivannan has two sons. The age of Manivannan is three times the sum of the ages of his two sons. Five years hence, his age will be double the sum of the ages of his two sons. What is the present age of Manivannan?

a) 45 years b) 33 years c) 48 years d) 54 years

Answer : a) 45 years.

Solution :

Let the sum of the present ages of two sons of Manivannan be S.
Then, Manivannan’s present age = 3S years ----> 1
Five years hence, his age will be double the sum of the ages of his two sons. After 5 years the sum of the ages of son will be S + 10 ----> 2 (adding 5 years to each of the two sons)

According to above condition,
Manivannan’s Age after 5 years = 2 ( Sum of the ages of the two sons after 5 years )
Manivannan’s Present Age + 5 = 2 ( Sum of the ages of the two sons after 5 years )

Substituting values from 1 and 2 on above equation we get,
(3S +5) = 2(S+10) => 3S +5 = 2S + 20 => S = 15

Hence present age of Manivannan = 3 S = 3 x 15 = 45 years.