A father is 3 times as old as his son. After 12 years, his age will be twice as that of his son then. Find their present ages.

Let the father's present age be $F$ years.
Let the son's present age be $S$ years.

From the first statement: "A father is 3 times as old as his son."

After 12 years:
Father's age will be $F+12$.
Son's age will be $S+12$.
From the second statement: "After 12 years, his age will be twice as that of his son then."

Substitute equation (1) into equation (2):

Subtract $2S$ from both sides:

Subtract 12 from both sides:

Now substitute the value of $S$ back into equation (1) to find $F$:

The father's present age is 36 years.
The son's present age is 12 years.

The present ages are:
Father: $\boxed{\text{36 years}}$
Son: $\boxed{\text{12 years}}$

2. The ages of 2 friends Annie and Niyu differ by 3 years. Annie's father Durram is twice as old as Annie and Niyu is twice as old as his sister Kathy. The ages of Kathy and Durram differ by 30 years. Find the ages of Annie and Niyu.

Let Annie's age be $A$.
Let Niyu's age be $N$.
Let Durram's age be $D$.
Let Kathy's age be $K$.

"The ages of 2 friends Annie and Niyu differ by 3 years." This means $|A - N| = 3$.
So, either $A - N = 3$ or $N - A = 3$.

"Annie's father Durram is twice as old as Annie."

"Niyu is twice as old as his sister Kathy."

"The ages of Kathy and Durram differ by 30 years." Since Durram is a father and Kathy is a sister, it is logical that Durram is older than Kathy.

Substitute equations (1) and (2) into equation (3):

Multiply the entire equation by 2 to eliminate the fraction:

Now we consider the two possible cases for the age difference between Annie and Niyu:

• Case 1: Annie is 3 years older than Niyu ($A - N = 3$) From $A - N = 3$, we can express $N$ as $N = A - 3$. Substitute this into equation (4):

  $$4A - (A - 3) = 60$$ $$4A - A + 3 = 60$$ $$3A + 3 = 60$$ $$3A = 60 - 3$$ $$3A = 57$$ $$A = \frac{57}{3}$$ $$A = 19$$

  Now find Niyu's age using $N = A - 3$:

  $$N = 19 - 3$$ $$N = 16$$

  Check this solution: If Annie is 19, Durram is $2 \times 19 = 38$. If Niyu is 16, Kathy is $16 / 2 = 8$. The difference between Durram and Kathy's ages is $38 - 8 = 30$, which matches the problem statement.

• Case 2: Niyu is 3 years older than Annie ($N - A = 3$) From $N - A = 3$, we can express $N$ as $N = A + 3$. Substitute this into equation (4):

  $$4A - (A + 3) = 60$$ $$4A - A - 3 = 60$$ $$3A - 3 = 60$$ $$3A = 60 + 3$$ $$3A = 63$$ $$A = \frac{63}{3}$$ $$A = 21$$

  Now find Niyu's age using $N = A + 3$:

  $$N = 21 + 3$$ $$N = 24$$

  Check this solution: If Annie is 21, Durram is $2 \times 21 = 42$. If Niyu is 24, Kathy is $24 / 2 = 12$. The difference between Durram and Kathy's ages is $42 - 12 = 30$, which also matches the problem statement.

There are two possible sets of ages for Annie and Niyu that satisfy all conditions:

• Possibility 1: Annie is $\boxed{\text{19 years old}}$ and Niyu is $\boxed{\text{16 years old}}$.
• Possibility 2: Annie is $\boxed{\text{21 years old}}$ and Niyu is $\boxed{\text{24 years old}}$.