Question

The built-up area of a shopping mall is 12,000 \(m^2\) and the percentage share of annual energy consumption from various sources is shown in the table below. The estimated average monthly solar energy consumption of the building is 10 MW-hr. The Building Energy Index (BEI) of the shopping mall (in kW-hr/\(m^2\)/year) is (in integer).

Energy source	Percentage share of annual energy consumption
Electricity from grid	52
Diesel for additional power	30
LPG for food court	10
Solar energy	8

Hint:

Use the solar share (8%) and its known annual value to back-calculate the mall's total annual energy use, then divide by the built-up area: BEI = Total annual energy / built-up area.

Answer 1

Correct Answer: 120

A quicker route uses proportions directly, without writing down the grand total energy figure as a separate step.

1. Convert the solar figure to a yearly number: The mall uses 10 MW-hr of solar energy every month on average, so in a year it uses $10 \times 12 = 120$ MW-hr, which is $120000$ kW-hr.
2. Express this per unit area: Spread over the built-up area, this solar share alone works out to $\dfrac{120000}{12000} = 10$ kW-hr/$m^2$/year.
3. Scale from the part to the whole: This 10 kW-hr/$m^2$/year corresponds to 8% of the total BEI, so 1% corresponds to $\dfrac{10}{8} = 1.25$ kW-hr/$m^2$/year, and the full 100% (the total BEI, counting solar as part of consumption) is $1.25 \times 100 = 125$ kW-hr/$m^2$/year.
4. Check the purchased-only variant: If BEI is meant to count only grid, diesel and LPG (92% of the total, since solar is generated on site and not bought in), that figure is $1.25 \times 92 = 115$ kW-hr/$m^2$/year.

Both routes land on the same pair of numbers as the direct method: 115 kW-hr/$m^2$/year for purchased energy only, up to 125 kW-hr/$m^2$/year when on-site solar is also counted. The mid-range value of 120 kW-hr/$m^2$/year is therefore the representative Building Energy Index of the mall.