Solve the following problems using the indicated strategy.

The company uses $200 \text{ kg}$ in the first step and $300 \text{ kg}$ in the second step.

The amount of raw material used in each step is $\boxed{\text{First step: } 200 \text{ kg, Second step: } 300 \text{ kg}}$.

2.

She gives half of this amount to her sister. To find the fraction her sister receives, multiply Mary's fraction by $\frac{1}{2}$.

Mary's sister receives $\frac{1}{8}$ of the cake.

The fraction of the cake her sister receives is $\boxed{\frac{1}{8}}$.

3.

The fraction of large size t-shirts is $\frac{3}{5}$. To find the number of large t-shirts, multiply the total number of t-shirts by this fraction.

Royce bought 12 large size t-shirts.

The number of large size t-shirts Royce bought is $\boxed{12}$.

4.

Day 1: $\frac{1}{3} \times \text{P}150.00 = \text{P}50.00$
Day 2: $\frac{2}{3} \times \text{P}300.00 = \text{P}200.00$
Day 3: $\frac{4}{3} \times \text{P}600.00 = \text{P}800.00$

The numerator of the fraction doubles each day ($1 \to 2 \to 4$).
The base amount doubles each day ($\text{P}150 \to \text{P}300 \to \text{P}600$).

For Day 4, the numerator will be $4 \times 2 = 8$, so the fraction is $\frac{8}{3}$.
For Day 4, the base amount will be $\text{P}600 \times 2 = \text{P}1200.00$.

Her daughter earned P3200.00 for the 4th day's work.

The amount her daughter earned for the 4th day's work is $\boxed{\text{P}3200.00}$.

5.

Fraction red = $\frac{1}{4}$
Fraction yellow = $\frac{1}{4}$
Total fraction of red and yellow = $\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

The remaining clips are blue.
Fraction blue = $1 - \text{Fraction of red and yellow}$
Fraction blue = $1 - \frac{1}{2} = \frac{1}{2}$

There are 30 blue clips.

The number of blue clips is $\boxed{30}$.