Basics of Financial Mathematics — NCERT Solutions

Step 1: Calculate daily energy consumption of each appliance

(i) TV:
$$\text{Energy} = \frac{4 \times 85}{1000} = \frac{340}{1000} = 0.34 \text{ kWh/day}$$

(ii) Toaster:
$$\text{Energy} = \frac{15}{60} \times \frac{1000}{1000} = 0.25 \text{ kWh/day}$$

(iii) Kettle:
$$\text{Energy} = \frac{2400 \times 2}{1000} = 4.8 \text{ kWh/day}$$

(iv) 15 Light Bulbs:
$$\text{Energy} = \frac{15 \times 5 \times 100}{1000} = 7.5 \text{ kWh/day}$$

Step 2: Total Daily Usage

$$\text{Total} = 0.34 + 0.25 + 4.8 + 7.5 = 12.89 \text{ kWh/day}$$

Step 3: Monthly Usage (30 days)

$$\text{Monthly Usage} = 30 \times 12.89 = 386.7 \text{ kWh/month}$$

Step 4: Usage Charge

$$\text{Usage Charge} = 386.7 \times 22 \text{ cts} = 8507.4 \text{ cts} = ₹85.07$$

Step 5: Line Charge

$$\text{Line Charge} = ₹1.10 \times 30 = ₹33.00$$

Step 6: Total Monthly Bill

$$\text{Total Bill} = ₹85.07 + ₹33.00 = \boxed{₹118.07}$$

$$\therefore \text{The total electricity bill for the month is } \mathbf{₹118.07}.$$

Given:

• Service Charge = ₹40/month (build-up area ≤ 200 sq. m)
• Consumption Charges:
• 0 – 6,000 litres → NIL
• 7,001 – 20,000 litres → ₹2 per litre (for units above 6,000)
• 21,001 – 30,000 litres → ₹7 per litre (for units in this slab)
• Above 30,000 litres → ₹10 per litre (for units above 30,000)
• Sewage Charge = 50% of Consumption Charge

(a) Consumption = 6,000 litres

$$\text{Service Charge} = ₹40$$
$$\text{Consumption Charge} = ₹0 \text{ (NIL for 0–6000 litres)}$$
$$\text{Sewage Charge} = 50\% \times 0 = ₹0$$
$$\text{Total Bill} = ₹40 + 0 + 0 = \boxed{₹40}$$

(b) Consumption = 10,000 litres

$$\text{Service Charge} = ₹40$$
$$\text{Consumption Charge} = (10,000 - 6,000) \times ₹2 = 4,000 \times 2 = ₹8$$

(First 6,000 litres are free; next 4,000 litres @ ₹2 each)

$$\text{Sewage Charge} = 50\% \times ₹8 = ₹4$$
$$\text{Total Bill} = ₹40 + ₹8 + ₹4 = \boxed{₹52}$$

(c) Consumption = 20,000 litres

$$\text{Service Charge} = ₹40$$
$$\text{Consumption Charge} = (20,000 - 6,000) \times ₹2 = 14,000 \times 2 = ₹28$$

(First 6,000 litres free; next 14,000 litres @ ₹2 each)

$$\text{Sewage Charge} = 50\% \times ₹28 = ₹14$$
$$\text{Total Bill} = ₹40 + ₹28 + ₹14 = \boxed{₹82}$$

(d) Consumption = 21,000 litres

$$\text{Service Charge} = ₹40$$

Consumption Charge:

• First 6,000 litres → NIL
• Next 14,000 litres (6,001 to 20,000) @ ₹2 = ₹28
• Next 1,000 litres (20,001 to 21,000) @ ₹7 = ₹7

$$\text{Total Consumption Charge} = ₹28 + ₹7 = ₹35$$

$$\text{Sewage Charge} = 50\% \times ₹35 = ₹17.50$$

$$\text{Total Bill} = ₹40 + ₹35 + ₹17.50 = \boxed{₹92.50 \approx ₹93}$$

(e) Consumption = 31,000 litres

$$\text{Service Charge} = ₹40$$

Consumption Charge:

• First 6,000 litres → NIL
• Next 14,000 litres (6,001 to 20,000) @ ₹2 = ₹28
• Next 10,000 litres (20,001 to 30,000) @ ₹7 = ₹70
• Next 1,000 litres (30,001 to 31,000) @ ₹10 = ₹10

$$\text{Total Consumption Charge} = ₹28 + ₹70 + ₹10 = ₹108$$

$$\text{Sewage Charge} = 50\% \times ₹108 = ₹54$$

$$\text{Total Bill} = ₹40 + ₹108 + ₹54 = \boxed{₹202}$$

Summary Table: