Determine the force required to lift the mass.

The force ($F$) needed to lift the mass is equal to its weight.

$$F = m \cdot g$$

Given:

• Mass ($m$) = $20 \text{ kg}$
• Acceleration due to gravity ($g$) = $10 \text{ m/s}^2$

$$F = 20 \text{ kg} \times 10 \text{ m/s}^2$$ $$F = 200 \text{ N}$$

Power ($P$) is the product of force and velocity.

$$P = F \cdot v$$

Given:

• Force ($F$) = $200 \text{ N}$
• Velocity ($v$) = $5 \text{ m/s}$

$$P = 200 \text{ N} \times 5 \text{ m/s}$$ $$P = 1000 \text{ W}$$

The power developed by the boy is $1000 \text{ W}$. This corresponds to option (D).

The final answer is $\text{D) } 1000 \text{W}$.