In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main supply is 220 V. The minimum fuse capacity (rated value) of the building will be:

We begin by noting that the electric fuse has to carry the total current drawn by all the appliances that may be switched on together. The current is obtained from power with the well-known relation:

$$P = VI$$

where $$P$$ is the electric power in watts (W), $$V$$ is the supply voltage in volts (V) and $$I$$ is the current in amperes (A). Rearranging the formula, we obtain

$$I = \dfrac{P}{V}$$

To use this expression, we first calculate the total power consumption of the building by adding the power ratings of every device present.

We have 15 bulbs rated at 45 W each. So their combined power is

$$P_1 = 15 \times 45\ \text{W} = 675\ \text{W}$$

Now, 15 bulbs are rated at 100 W each. Hence

$$P_2 = 15 \times 100\ \text{W} = 1500\ \text{W}$$

Next, 15 small fans are rated at 10 W each, giving

$$P_3 = 15 \times 10\ \text{W} = 150\ \text{W}$$

Finally, there are 2 heaters, each of 1 kW. Remembering that $$1\ \text{kW}=1000\ \text{W}$$, we write

$$P_4 = 2 \times 1\ \text{kW} = 2 \times 1000\ \text{W} = 2000\ \text{W}$$

Adding all these powers gives the total power demand:

$$\begin{aligned} P_{\text{total}} &= P_1 + P_2 + P_3 + P_4 \\ &= 675\ \text{W} + 1500\ \text{W} + 150\ \text{W} + 2000\ \text{W} \\ &= 4325\ \text{W} \end{aligned}$$

The supply voltage of the mains is given as 220 V. Substituting $$P_{\text{total}}$$ and $$V=220\ \text{V}$$ in the rearranged power formula, we get the total current:

$$\begin{aligned} I_{\text{total}} &= \dfrac{P_{\text{total}}}{V} \\ &= \dfrac{4325\ \text{W}}{220\ \text{V}} \\ &= 19.659\ \text{A} \end{aligned}$$

Numerically, this equals approximately $$19.7\ \text{A}$$. A fuse is chosen so that its rating is just above the maximum expected current; if it were below, the fuse would blow during normal operation. The next available standard rating higher than $$19.7\ \text{A}$$ is $$20\ \text{A}$$.

Hence, the correct answer is Option D.