Class 11 Applied Mathematics

Utility
Bills & Tariffs

Deconstructing the math behind your monthly expenses—from electricity slabs to volumetric water usage and natural gas tariffs.

Billing Fundamentals

Concepts of Consumption

Tariff

Tariff is the rate or pricing structure at which a utility service provider charges customers for use.

Fixed Charge

A mandatory monthly fee independent of consumption level, covering maintenance and operational costs.

Surcharge

An additional charge levied on the base bill, often to recover specific costs like energy taxes or infrastructure upgrades.

Electricity Billing

ℹ️

Energy Charges (Slabs)

Electricity is usually billed using a **progressive slab system**. The rate per unit increases as your consumption crosses specific thresholds. This encourages energy conservation.

Sample Tariff Structure

0 - 200 units₹3.00 / unit

201 - 400 units₹4.50 / unit

Above 400 units₹6.50 / unit

The Formula

Electricity Expenditure Model

Total Bill =

Energy + Fixed + Surcharge + Tax

Electricity Bill Visualizer

Simulate slab-based billing with taxes and surcharges.

Units Consumed: 250 kWh

0 units1000 units

Consumption Slab Impact

0-200

₹3/u

201-400

₹4.5/u

400+

₹6.5/u

Total Bill Estimate

₹1082.25

Energy Charges:₹825.00

Fixed Charge:₹150.00

Surcharge (8%):₹66.00

Energy Tax (5%):₹41.25

Final Payable:₹1082.25

Calculation LogicThe bill is calculated in stages. First, the energy charge is found using progressive slabs. Then, surcharges and taxes are applied to either the base charge or the total energy consumption.

Solving Electricity Bills

Consider a family that used **450 units** in a month. Let the fixed charge be **₹150**, energy tax be **5%**, and slabs be: ₹3 (0-200), ₹4.5 (201-400), ₹6 (400+).

Stage 1: Slab 1

200 \times 3 = \text{₹}600

Stage 2: Slab 2

200 \times 4.5 = \text{₹}900

Stage 3: Slab 3

50 \times 6 = \text{₹}300

Energy Total₹1,800

Taxes & Charges:

Fixed: ₹150

Tax: 5% of

1,800

\text{₹}90

Grand Total

₹2,040

Water & Natural Gas

ℹ️

Water Billing (kl)

Measured in kilolitres. Apart from usage, it often includes a **Sewerage Charge** which is a fixed percentage (60%-100%) of your water consumption charge.

Water Charges Formula

Bill =

(kl \times Rate) + Sewerage + Tax + Rent

❗

PNG (Gas) Tariffs

Piped Natural Gas is measured in SCM (Standard Cubic Meter). It typically has a fixed service charge plus consumption rates that may vary between domestic and commercial users.

PNG Billing Formula

Bill =

(SCM \times Tariff) + Fee + VAT

Water Meter

kl (Kilolitre) Consumption

Usage: 25 kl

Base Charge (₹12/kl):₹300.00

Sewerage (60%):₹180.00

Water Tax (20%):₹60.00

Total Payable:₹540.00

PNG Terminal

SCM Consumption

Usage: 30 SCM

Energy (₹45/SCM):₹1350.00

Fixed Service Charge:₹100.00

Estimate Total:₹1450.00

Technical Glossary

Connection Fee

The initial one-time deposit or registration fee required to establish a utility account.

Security Deposit

A refundable amount held against potential defaults, often based on estimated monthly usage.

Master Illustration

Domestic PNG Calculation

A consumer uses 38 SCM of gas in a bi-monthly cycle. Current rate is ₹48/SCM. Fixed service charge is ₹150 and VAT is 12% on consumption charge.

1. Consumption Charge (38 × 48)₹1,824

2. VAT (12% of 1824)₹218.88

3. Net Total (1824 + 150 + 218.88)₹2,192.88

Security Deposit

Typically ₹5,000 for domestic connections, refundable upon termination.

Type: Domestic PNG

Audit Laboratory

Utility Analysis

8 Important Problems

CBSE Exam Type

Billing Analysis Zone

Find the electricity bill for 350 units if the tariff is: ₹3/unit for first 200 units, ₹4.5/unit for next 150 units. Fixed charge is ₹150 and surcharge is 8%.

✓ Show Solution

1. 0-200 units:

200 \times 3 = \text{₹}600

2. 201-350 units:

150 \times 4.5 = \text{₹}675

3. Total Energy Charge =

600 + 675 = \text{₹}1,275

4. Surcharge = 8% of

1,275

\text{₹}102

5. Total Bill = Energy + Fixed + Surcharge =

1,275 + 150 + 102 = \text{₹}1,527

MEDIUM

A household consumed 15 kl of water. If the rate is ₹10/kl and sewerage charge is 60% of water charge, calculate total bill including ₹20 meter rent.

✓ Show Solution

1. Water Charge =

15 \times 10 = \text{₹}150

2. Sewerage Charge =

60% \text{ of } 150 = \text{₹}90

3. Total Bill = Water + Sewerage + Rent =

150 + 90 + 20 = \text{₹}260

EASY

Calculate PNG bill for 42 SCM at ₹45/SCM if fixed charge is ₹100 and VAT is 5% on total amount.

✓ Show Solution

1. Gas Charge =

42 \times 45 = \text{₹}1,890

2. Base Amount =

1,890 + 100 = \text{₹}1,990

3. VAT =

5% \text{ of } 1,990 = \text{₹}99.50

4. Final Total =

1,990 + 99.50 = \text{₹}2,089.50

MEDIUM

Electricity meter reading: Previous 4560, Current 4910. Calculate units consumed.

✓ Show Solution

1. Units = Current - Previous =

4910 - 4560 = 350

units.

EASY

For a commercial shop, fixed charge is ₹500. Slabs: first 100 units @ ₹8, above 100 @ ₹10. Calculate bill for 150 units.

✓ Show Solution

1. 0-100:

100 \times 8 = \text{₹}800

2. 101-150:

50 \times 10 = \text{₹}500

3. Total = Energy + Fixed =

800 + 500 + 500 = \text{₹}1,800

MEDIUM

Water tax is levied at 10%. If water charge is ₹300, calculate total tax amount.

✓ Show Solution

1. Tax =

10% \text{ of } 300 = \text{₹}30

EASY

A factory uses 5000 units of electricity. Tariff is flat ₹7/unit with 10% energy tax. Find total.

✓ Show Solution

1. Energy =

5000 \times 7 = \text{₹}35,000

2. Tax =

10% \text{ of } 35,000 = \text{₹}3,500

3. Total = ₹38,500.

HARD

PNG security deposit is ₹5,000 (one-time). If monthly average bill is ₹800, how many months of consumption does the deposit cover roughly?

✓ Show Solution

5000 / 800 = 6.25

months.

EASY

Exam Insights

Board questions & Critical Applications

CBSE 2023

A residential complex consumes 1200 units. Slabs: 0-200 @ ₹3, 201-500 @ ₹4.5, 501-1000 @ ₹6, above 1000 @ ₹8. Fixed charge ₹200, Surcharge 8%. Calculate net payable.

Calculation Pathway1. 0-200:

200 \times 3 = 600

2. 201-500:

300 \times 4.5 = 1350

3. 501-1000:

500 \times 6 = 3000

4. 1001-1200:

200 \times 8 = 1600

5. Energy =

600 + 1350 + 3000 + 1600 = \text{₹}6,550

6. Surcharge =

8% \text{ of } 6550 = \text{₹}524

7. Total =

6550 + 200 + 524 = \text{₹}7,274

Theory Focus

Differentiate between fixed charge and consumption charge in utility bills with an example of an empty house.

Calculation Pathway1. Fixed charge is paid even with zero consumption. 2. In an empty house (0 units), the bill will still include the monthly fixed charge (e.g. ₹150).

Application Based

A consumer noticed 20% water tax and 60% sewerage charge on his bill of ₹400 (base charge). If he saves 10% water by fixing a leak, how much money is saved?

Calculation Pathway1. Initial Charge = ₹400. Total =

400 + 400(0.20) + 400(0.60) = 400 + 80 + 240 = \text{₹}720

2. New Charge (90%) = ₹360. New Total =

360 + 360(0.20) + 360(0.60) = 360 + 72 + 216 = \text{₹}648

3. Savings =

720 - 648 = \text{₹}72

CBSE 2022

Calculate PNG bill for 35 SCM @ ₹48/SCM with 12% VAT and ₹150 fixed charge.

Calculation Pathway1. Gas =

35 \times 48 = \text{₹}1,680

2. Total base =

1680 + 150 = \text{₹}1,830

3. VAT = 12% of

1830

\text{₹}219.60

4. Total = ₹2,049.60

General Awareness

Why is water usage measured in kilolitres (kl) instead of litres?

Calculation Pathway1. household usage is high; 1 kl = 1000 litres. Measuring in kl keeps the numbers manageable for billing (e.g., 25 kl vs 25,000 L).

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Class 11 Applied Mathematics

Utility
Bills & Tariffs

Deconstructing the math behind your monthly expenses—from electricity slabs to volumetric water usage and natural gas tariffs.

Billing Fundamentals

Concepts of Consumption

Tariff

Tariff is the rate or pricing structure at which a utility service provider charges customers for use.

Fixed Charge

A mandatory monthly fee independent of consumption level, covering maintenance and operational costs.

Surcharge

An additional charge levied on the base bill, often to recover specific costs like energy taxes or infrastructure upgrades.

Electricity Billing

ℹ️

Energy Charges (Slabs)

Electricity is usually billed using a **progressive slab system**. The rate per unit increases as your consumption crosses specific thresholds. This encourages energy conservation.

Sample Tariff Structure

0 - 200 units₹3.00 / unit

201 - 400 units₹4.50 / unit

Above 400 units₹6.50 / unit

The Formula

Electricity Expenditure Model

Total Bill =

Energy + Fixed + Surcharge + Tax

Electricity Bill Visualizer

Simulate slab-based billing with taxes and surcharges.

Units Consumed: 250 kWh

0 units1000 units

Consumption Slab Impact

0-200

₹3/u

201-400

₹4.5/u

400+

₹6.5/u

Total Bill Estimate

₹1082.25

Energy Charges:₹825.00

Fixed Charge:₹150.00

Surcharge (8%):₹66.00

Energy Tax (5%):₹41.25

Final Payable:₹1082.25

Solving Electricity Bills

Consider a family that used **450 units** in a month. Let the fixed charge be **₹150**, energy tax be **5%**, and slabs be: ₹3 (0-200), ₹4.5 (201-400), ₹6 (400+).

Stage 1: Slab 1

200 \times 3 = \text{₹}600

Stage 2: Slab 2

200 \times 4.5 = \text{₹}900

Stage 3: Slab 3

50 \times 6 = \text{₹}300

Energy Total₹1,800

Taxes & Charges:

Fixed: ₹150

Tax: 5% of

1,800

\text{₹}90

Grand Total

₹2,040

Water & Natural Gas

ℹ️

Water Billing (kl)

Measured in kilolitres. Apart from usage, it often includes a **Sewerage Charge** which is a fixed percentage (60%-100%) of your water consumption charge.

Water Charges Formula

Bill =

(kl \times Rate) + Sewerage + Tax + Rent

❗

PNG (Gas) Tariffs

Piped Natural Gas is measured in SCM (Standard Cubic Meter). It typically has a fixed service charge plus consumption rates that may vary between domestic and commercial users.

PNG Billing Formula

Bill =

(SCM \times Tariff) + Fee + VAT

Water Meter

kl (Kilolitre) Consumption

Usage: 25 kl

Base Charge (₹12/kl):₹300.00

Sewerage (60%):₹180.00

Water Tax (20%):₹60.00

Total Payable:₹540.00

PNG Terminal

SCM Consumption

Usage: 30 SCM

Energy (₹45/SCM):₹1350.00

Fixed Service Charge:₹100.00

Estimate Total:₹1450.00

Technical Glossary

Connection Fee

The initial one-time deposit or registration fee required to establish a utility account.

Security Deposit

A refundable amount held against potential defaults, often based on estimated monthly usage.

Master Illustration

Domestic PNG Calculation

A consumer uses 38 SCM of gas in a bi-monthly cycle. Current rate is ₹48/SCM. Fixed service charge is ₹150 and VAT is 12% on consumption charge.

1. Consumption Charge (38 × 48)₹1,824

2. VAT (12% of 1824)₹218.88

3. Net Total (1824 + 150 + 218.88)₹2,192.88

Security Deposit

Typically ₹5,000 for domestic connections, refundable upon termination.

Type: Domestic PNG

Audit Laboratory

Utility Analysis

8 Important Problems

CBSE Exam Type

Billing Analysis Zone

Find the electricity bill for 350 units if the tariff is: ₹3/unit for first 200 units, ₹4.5/unit for next 150 units. Fixed charge is ₹150 and surcharge is 8%.

✓ Show Solution

1. 0-200 units:

200 \times 3 = \text{₹}600

2. 201-350 units:

150 \times 4.5 = \text{₹}675

3. Total Energy Charge =

600 + 675 = \text{₹}1,275

4. Surcharge = 8% of

1,275

\text{₹}102

5. Total Bill = Energy + Fixed + Surcharge =

1,275 + 150 + 102 = \text{₹}1,527

MEDIUM

A household consumed 15 kl of water. If the rate is ₹10/kl and sewerage charge is 60% of water charge, calculate total bill including ₹20 meter rent.

✓ Show Solution

1. Water Charge =

15 \times 10 = \text{₹}150

2. Sewerage Charge =

60% \text{ of } 150 = \text{₹}90

3. Total Bill = Water + Sewerage + Rent =

150 + 90 + 20 = \text{₹}260

EASY

Calculate PNG bill for 42 SCM at ₹45/SCM if fixed charge is ₹100 and VAT is 5% on total amount.

✓ Show Solution

1. Gas Charge =

42 \times 45 = \text{₹}1,890

2. Base Amount =

1,890 + 100 = \text{₹}1,990

3. VAT =

5% \text{ of } 1,990 = \text{₹}99.50

4. Final Total =

1,990 + 99.50 = \text{₹}2,089.50

MEDIUM

Electricity meter reading: Previous 4560, Current 4910. Calculate units consumed.

✓ Show Solution

1. Units = Current - Previous =

4910 - 4560 = 350

units.

EASY

For a commercial shop, fixed charge is ₹500. Slabs: first 100 units @ ₹8, above 100 @ ₹10. Calculate bill for 150 units.

✓ Show Solution

1. 0-100:

100 \times 8 = \text{₹}800

2. 101-150:

50 \times 10 = \text{₹}500

3. Total = Energy + Fixed =

800 + 500 + 500 = \text{₹}1,800

MEDIUM

Water tax is levied at 10%. If water charge is ₹300, calculate total tax amount.

✓ Show Solution

1. Tax =

10% \text{ of } 300 = \text{₹}30

EASY

A factory uses 5000 units of electricity. Tariff is flat ₹7/unit with 10% energy tax. Find total.

✓ Show Solution

1. Energy =

5000 \times 7 = \text{₹}35,000

2. Tax =

10% \text{ of } 35,000 = \text{₹}3,500

3. Total = ₹38,500.

HARD

PNG security deposit is ₹5,000 (one-time). If monthly average bill is ₹800, how many months of consumption does the deposit cover roughly?

✓ Show Solution

5000 / 800 = 6.25

months.

EASY

Exam Insights

Board questions & Critical Applications

CBSE 2023

A residential complex consumes 1200 units. Slabs: 0-200 @ ₹3, 201-500 @ ₹4.5, 501-1000 @ ₹6, above 1000 @ ₹8. Fixed charge ₹200, Surcharge 8%. Calculate net payable.

Calculation Pathway1. 0-200:

200 \times 3 = 600

2. 201-500:

300 \times 4.5 = 1350

3. 501-1000:

500 \times 6 = 3000

4. 1001-1200:

200 \times 8 = 1600

5. Energy =

600 + 1350 + 3000 + 1600 = \text{₹}6,550

6. Surcharge =

8% \text{ of } 6550 = \text{₹}524

7. Total =

6550 + 200 + 524 = \text{₹}7,274

Theory Focus

Differentiate between fixed charge and consumption charge in utility bills with an example of an empty house.

Calculation Pathway1. Fixed charge is paid even with zero consumption. 2. In an empty house (0 units), the bill will still include the monthly fixed charge (e.g. ₹150).

Application Based

A consumer noticed 20% water tax and 60% sewerage charge on his bill of ₹400 (base charge). If he saves 10% water by fixing a leak, how much money is saved?

Calculation Pathway1. Initial Charge = ₹400. Total =

400 + 400(0.20) + 400(0.60) = 400 + 80 + 240 = \text{₹}720

2. New Charge (90%) = ₹360. New Total =

360 + 360(0.20) + 360(0.60) = 360 + 72 + 216 = \text{₹}648

3. Savings =

720 - 648 = \text{₹}72

CBSE 2022

Calculate PNG bill for 35 SCM @ ₹48/SCM with 12% VAT and ₹150 fixed charge.

Calculation Pathway1. Gas =

35 \times 48 = \text{₹}1,680

2. Total base =

1680 + 150 = \text{₹}1,830

3. VAT = 12% of

1830

\text{₹}219.60

4. Total = ₹2,049.60

General Awareness

Why is water usage measured in kilolitres (kl) instead of litres?

Calculation Pathway1. household usage is high; 1 kl = 1000 litres. Measuring in kl keeps the numbers manageable for billing (e.g., 25 kl vs 25,000 L).