The table shows the ages in years of 42 children at a birthday party. (a) Find the value of x. (b) Calculate, correct to the nearest whole number, the mean age. (c) Find the probability of selecting at random a child whose age is not less than 9 years.

Labour cost increased by $2y\%$:

$$L_1 = L_0 \left(1 + \frac{2y}{100}\right) = 30,000 \left(1 + \frac{2y}{100}\right)$$

Materials cost increased by $2.5y\%$:

$$M_1 = M_0 \left(1 + \frac{2.5y}{100}\right) = 72,000 \left(1 + \frac{2.5y}{100}\right)$$

Consultancy fee remained unchanged:

$$C_1 = C_0 = \text{GHe } 18,000$$

The new cost of labour is two-fifth the new cost of materials:

$$L_1 = \frac{2}{5} M_1$$ $$30,000 \left(1 + \frac{2y}{100}\right) = \frac{2}{5} \times 72,000 \left(1 + \frac{2.5y}{100}\right)$$ $$30,000 \left(1 + \frac{2y}{100}\right) = 28,800 \left(1 + \frac{2.5y}{100}\right)$$

Divide both sides by 100:

$$300 \left(1 + \frac{2y}{100}\right) = 288 \left(1 + \frac{2.5y}{100}\right)$$

Divide both sides by 12:

$$25 \left(1 + \frac{2y}{100}\right) = 24 \left(1 + \frac{2.5y}{100}\right)$$ $$25 + \frac{50y}{100} = 24 + \frac{60y}{100}$$ $$25 + 0.5y = 24 + 0.6y$$ $$25 - 24 = 0.6y - 0.5y$$ $$1 = 0.1y$$ $$y = \frac{1}{0.1}$$ $$y = 10$$

The value of $y$ is $\boxed{\text{10}}$.

$$\text{New Total Cost} = L_1 + M_1 + C_1$$ $$\text{New Total Cost} = 36,000 + 90,000 + 18,000 = \text{GHe } 144,000$$

The new cost of building the house is $\boxed{\text{GHe 144,000.00}}$.