Problem on Ages :

1. The age of a mother is 4 times the age of her son. If 5 years ago mother’s age was 7 times the age of her son at that time, what is mother’s present age ?

Solution : The mother’s present age

= ( n₁−1/n₁−n₂)n₂t [Here, n₁ =7, n₂ = 4 and t= 5]

=(7−1/7−4) 4×5 = 6×4×5/3 = 40 years.

2. The age of Sunny is four times the age of his son. After ten years, the age of sunny will be only twice the age of his son. Find the present age of sunny’s son.

Solution : The present age of Sunny’s son

[Here, n₁ =4, n₂ = 2 and t=10]

= (n₂ −1/ n₁−n₂)t

= (2−1/4−2)10

= 5 years.

3. 10 years ago Kavita’s mother was 4 times older than her daughter. After 10 years, the mother will be twice older than the daughter. Find the present age of Kavita.

Solution : Present age of Kavita

[Here, n₁ =4, n₂ = 2, t₁=10 and t₂= 10]

= t₂(n₂ −1)+ t₁(n₁−1 )/ n₁−n₂

= 10(2−1)+10(4−1)/4−2

=10+30/2

4. The ratio of the age of mother and daughter at present is 6:1. After 5 years, the ratio will become 7:2. Find the present age of the daughter.

Solution : The present age of the

Daughter =bt(c−d)/ad−bc

[Here, a=6, b=1, c=7, d=2 and t=5]

= 1×5(7−2)/6×2−1×7

= 5 years.

5. The ages of Jotin and Mohon differ by 16 years. Six years ago, Mohon’s age was thrice as that of Jotin’s, find their present ages.

Solution : Let Jotin’s age = X years

So, Mohon’s age = (X + 16 ) years

Also, 3 (X – 6) = X + 16 – 6 or, X=14

∴ Jotin’s age = 14 years

and, Mohon’s age = 14+16 = 30 years.