To solve this problem, we need to calculate the minimum energy input required by the induction furnace to melt 100 kg of steel, given the efficiency and the energy requirement per ton of steel.

First, we need to understand the energy needed in this scenario. The problem states that the energy required to melt steel is 1500 \text{ kWh/ton}, which means that for one ton (or 1000 kg) of steel, 1500 kWh is required.

Given:

• The mass of steel to be melted, m = 100 \text{ kg}
• Efficiency of the furnace, \eta = 60\% = 0.6

Since we are melting 100 kg of steel, which is \frac{100}{1000} = 0.1 tons, we can calculate the energy required to melt this amount without considering efficiency as follows:

Energy required (output) = 1500 \text{ kWh/ton} \times 0.1 \text{ ton} = 150 \text{ kWh}

However, since the furnace is not 100% efficient, more energy is required to achieve the 150 kWh output. The actual (input) energy required is calculated based on the efficiency:

\text{Energy input} = \frac{\text{Energy required (output)}}{\text{Efficiency}} = \frac{150}{0.6} = 250 \text{ kWh}

Thus, the minimum energy input needed for the furnace is 250 kWh. Therefore, the correct answer is:

250 kWh