Question

The ages of two friends Manjit and Ranjit differ by 3 years. Manjit's father Dharam is twice as old as Manjit and Ranjit as twice as old as his sister Jaspreet. The ages of Jaspreet and Dharam differ by 30 years. Find the ages of Manjit and Ranjit.

Answer 1

Given data:

The age difference between Manjit (M) and Ranjit (R) is 3 years: M - R = 3
Manjit's father, Dharam (D), is twice as old as Manjit: D = 2M
Ranjit is twice as old as his sister, Jaspreet (J): R = 2J
The age difference between Dharam and Jaspreet is 30 years: D - J = 30
Equations:

M - R = 3
D = 2M
R = 2J
D - J = 30
Solutions:
By substituting the expressions for M, R, and D, we can solve the system of equations:

Substituting D = 2M into equation 4, we have:
2M - J = 30

Substituting R = 2J into equation 1, we have:
M - 2J = 3

Now, let's clarify the meaning of the variables:

M represents the age of Manjit.
R represents the age of Ranjit.
D represents the age of Dharam.
J represents the age of Jaspreet.

Using the above clarifications, we can solve the system of equations as follows:

From equation 2, we have D = 2M.
Substituting D = 2M into equation 4:
2M - J = 30

From equation 3, we have R = 2J.
Substituting R = 2J into equation 1:
M - 2J = 3

Solving the system of equations, we find:
J = 8
M = 19
R = 16

Therefore, the ages are as follows:
Manjit (M) is 19 years old.
Ranjit (R) is 16 years old.
Dharam (D) is 38 years old.
Jaspreet (J) is 8 years old.