Explain what a tariff is in this context and calculate the total units of electricity purchased given an initial meter reading and a purchase amount.

The initial meter reading before purchase was $5.3 \text{ kWh}$.
Lebogang purchased electricity worth $\text{R}398.00$.

The first tariff block is for $0-100 \text{ kWh}$ at $\text{R}2.775755$ per unit.
Units remaining in the first block = $100 \text{ kWh} - 5.3 \text{ kWh} = 94.7 \text{ kWh}$.
Cost of these units = $94.7 \text{ kWh} \times \text{R}2.775755/\text{kWh} = \text{R}262.7709985$.

Money remaining = $\text{R}398.00 - \text{R}262.7709985 = \text{R}135.2290015$.

The second tariff block is for $101-400 \text{ kWh}$ at $\text{R}3.248405$ per unit.
Units purchased in the second block = $\frac{\text{R}135.2290015}{\text{R}3.248405/\text{kWh}} \approx 41.6300 \text{ kWh}$.

Total units purchased = $94.7 \text{ kWh} + 41.6300 \text{ kWh} = 136.3300 \text{ kWh}$.

New meter reading = Initial meter reading + Total units purchased
New meter reading = $5.3 \text{ kWh} + 136.3300 \text{ kWh} = 141.6300 \text{ kWh}$.

Rounded new meter reading = $142 \text{ kWh}$.
The meter reading after purchase shown in Table 3 is $142.4 \text{ kWh}$. When rounded to the nearest whole number, $142.4 \text{ kWh}$ becomes $142 \text{ kWh}$.
Therefore, the meter reading after purchase is correct when rounded to the nearest whole number.

b)

The tariffs are VAT inclusive. Assuming the standard South African VAT rate of $15\%$.

The total purchase amount of $\text{R}398.00$ includes VAT.
VAT amount = $\frac{\text{VAT rate}}{1 + \text{VAT rate}} \times \text{Total amount}$
VAT amount = $\frac{0.15}{1 + 0.15} \times \text{R}398.00$
VAT amount = $\frac{0.15}{1.15} \times \text{R}398.00$
VAT amount = $\text{R}51.91304...$

The VAT amount on her electricity purchase is $\boxed{\text{R}51.91}$.