Household Arithmetic

You already know the three tools this unit needs: the unitary method (find the value of one, then of many), percentages (a discount, a fine, a tax) and adding a percentage to an amount. Try these first.

Each of those steps comes back in every bill below: a rate for one unit times the number of units, then a percentage taken off or added on. Most of these bills can be paid today through a bank’s app or a digital wallet such as eSewa or Khalti, without standing in a queue at the office; the arithmetic behind them is the same.

Electricity is measured in units. One unit is one kilowatt-hour (kWh): the energy a 1,000-watt heater uses in one hour, or a 10-watt LED bulb in 100 hours. The meter on the wall counts units the way a car counts kilometers: it only ever goes up. Each month the meter reader notes the number, and

$$\text{units used} = \text{present reading} - \text{previous reading}$$

The rates are set by the Electricity Regulatory Commission and published by the Nepal Electricity Authority (NEA). Since its decision of 2078/7/8 (Kartik 2078), still the tariff NEA gives for homes in November 2026, a single-phase home pays:

The minimum charge each month (Rs)

Units used in the month	5 A	15 A	30 A	60 A
0–20	30	50	75	125
21–30	50	75	100	125
31–50	50	75	100	125
51–100	75	100	125	150
101–250	100	125	150	200
over 250	150	175	200	250

The energy charge per unit (Rs)

Units	5 A	15 A	30 A	60 A
1–20	0 (see below)	4.00	5.00	6.00
21–30	6.50	6.50	6.50	6.50
31–50	8.00	8.00	8.00	8.00
51–250	9.50	9.50	9.50	9.50
over 250	11.00	11.00	11.00	11.00

On a 5 A meter, a home that uses 20 units or less pays no energy charge at all, only the Rs 30 minimum. A 5 A home that uses more than 20 units pays Rs 3 a unit for its first 20.

How a bill is worked out

The bill is the minimum charge plus the energy charge, and the energy charge is worked out block by block, like income tax in Unit 2: each rate is paid only on the units inside its block. For a 5 A meter:

Units used	Minimum charge	Energy charge
up to 20	Rs 30	none
21 to 30	Rs 50	first 20 at Rs 3, the rest at Rs 6.50
31 to 50	Rs 50	20 at Rs 3, 10 at Rs 6.50, the rest at Rs 8
51 to 100	Rs 75	20 at Rs 3, 10 at Rs 6.50, 20 at Rs 8, the rest at Rs 9.50
101 to 250	Rs 100	20 at Rs 3, 10 at Rs 6.50, 20 at Rs 8, the rest at Rs 9.50
over 250	Rs 150	20 at Rs 3, 10 at Rs 6.50, 20 at Rs 8, 200 at Rs 9.50, the rest at Rs 11

The 15, 30 and 60 A meters are billed the same way, with their own minimum charges and their own rate for the first 20 units.

$$\text{Bill} = \text{minimum charge} + \text{energy charge}$$

Move the units and see each block fill. Then change the meter.

Paying early, paying late

The bill is counted from the date the meter was read:

Paid on	Discount or fine
day 1 to 7	2% discount
day 8 to 15	the bill as it is
day 16 to 30	5% fine
day 31 to 40	10% fine
day 41 to 60	25% fine
after day 60	the line can be cut off without notice; the amount owed is recovered like money owed to the government, and reconnecting costs Rs 500

Back to Aayush’s bill

Aayush’s 60 units: minimum Rs 75 (51–100 block); energy 20 × 3 + 10 × 6.50 + 20 × 8 + 10 × 9.50 = 60 + 65 + 160 + 95 = 380; bill Rs 455.

His 120 units: minimum Rs 100 (101–250 block); energy 60 + 65 + 160 + 70 × 9.50 = 950; bill Rs 1,050. Paid within 7 days, 1050 × 0.98 = Rs 1,029.

The meter reader was right. The second 60 units were all charged at Rs 9.50, the dearest rate he reached, while the first 60 included 30 cheaper units; and the minimum charge rose from Rs 75 to Rs 100 as the month moved into the next block. So twice the units cost about 2.3 times as much.

Question 1

A 5 A meter is installed in Dambar Kumari’s house. Its readings at the end of each month of 2078 are:

Month	Kartik	Mangsir	Poush	Magh	Falgun
Meter reading	3528	3593	3700	3904	3980

Question 2

Using the tariff in this unit, find the amount paid to the Nepal Electricity Authority in each case.

Water through a metered tap is measured in liters, and charged by the unit: 1 unit = 1,000 liters, as much as a 1,000-liter roof tank holds. In the Kathmandu Valley the supplier is Kathmandu Upatyaka Khanepani Limited (KUKL).

KUKL’s tariff for metered taps has been the same since Shrawan 1, 2070, and its annual report for 2081/82 still gives it:

Pipe size	Minimum water (liters)	Minimum units	Minimum charge (Rs)	Each extra unit (Rs)
½ inch	10,000	10	100	32
¾ inch	27,000	27	1,910	71
1 inch	56,000	56	3,960	71
1½ inch	1,55,000	155	10,950	71
2 inch	3,20,000	320	22,600	71
3 inch	8,81,000	881	62,240	71
4 inch	18,10,000	1,810	1,27,865	71

The minimum charge pays for the minimum units, used or not; each unit above them is charged at the last column’s rate. On top of the water charge, a sewerage charge of 50% of it is added for the sewers KUKL looks after.

$$\begin{aligned} \text{Water charge} &= \text{minimum charge} + \text{extra units} \times \text{rate} \\ \text{Bill} &= \text{water charge} + 50\% \text{ of the water charge} \end{aligned}$$

Paying, counted from the day the bill is handed out:

Paid	Discount or fine
in the first or second month	3% discount
in the third month	the bill as it is
in the fourth month	10% fine
in the fifth month	20% fine
after the fifth month	50% fine

Question 1

Januka’s house has a ½ inch pipe. In Shrawan the present reading is 4225 and the previous reading 4197.

Question 2

A hotel used 423 units in a month through a 1½ inch pipe.

On a landline, the first 175 calls of a month cost Rs 200 together (the monthly minimum), and each call after that costs Re 1. On that total charge (TC), the government takes two charges, one after the other:

• the telecom service charge (TSC), 13% of the TC;
• value added tax (VAT), 13% of the TC and the TSC together.

$$\begin{aligned} \text{TC} &= 200 + (\text{calls} - 175) \times 1 \\ \text{TSC} &= 13\% \text{ of TC} \\ \text{VAT} &= 13\% \text{ of (TC + TSC)} \\ \text{Total} &= \text{TC} + \text{TSC} + \text{VAT} \end{aligned}$$

A call within the same area code is counted as one call for each 2 minutes; a call to another area code as one call for each minute.

Mobile phones have their own rates. Nepal Telecom’s, as its site gives them in November 2026, without taxes:

GSM prepaid	Rate
Call to an NT number	Rs 1.50 a minute
Call to another network	Rs 2 a minute
Video call	Rs 2 a minute
SMS	Re 1 (to NT), Rs 1.25 (to other networks)
Friends and family (up to 5 numbers)	Rs 0.70 a minute

GSM postpaid	Rate
Monthly rental	Rs 300 (with Rs 300 of talk time in it)
Call to an NT number	Re 1 a minute from 6 AM to 10 PM; Rs 0.55 from 10 PM to 6 AM
Call to another network	Rs 1.50 a minute
Friends and family (up to 5 numbers)	Rs 0.55 a minute

Every one of these rates is before taxes. From Shrawan 1, 2075 the TSC and VAT were 13% each, and a 2% ownership tax (OT) was added on postpaid bills and mobile recharges from Shrawan 1, 2077. Under the Finance Act 2082 the TSC is reported to be 10% now (the Nepal Telecommunications Authority’s notice of Baishakh 2083, as the news gave it); we could not read the Act or the notice ourselves, so take 10% as unconfirmed. The questions below use the rate each one states.

Question 1

Salim’s landline read 3992 at the end of Chaitra and 4444 at the end of Baishakh. The first 175 calls cost Rs 200 and each call after that Re 1.

Question 2

The first 175 calls cost Rs 200 and each call after that Re 1. Find the total with 13% TSC and 13% VAT for:

Question 3

The first 175 calls cost Rs 200 and each call after that Re 1. How many calls can be made for these amounts, without the TSC and VAT?

Question 4

Question 5

In towns, taxis may or may not run by the meter. A metered fare is the same for everyone, and the chance of being cheated is low. If a fare seems wrong, you can complain to the nearest traffic police office with the taxi’s number.

The meter starts at a fixed amount and then adds a set amount for every 200 meters. These are the fares the Department of Transport Management set on 2075/06/07, as the Nepal Bureau of Standards and Metrology posted them:

	Day (6 AM to 9 PM)	Night (9 PM to 6 AM)
Starting charge	Rs 14	Rs 21
Each 200 m	Rs 7.80 (Rs 39 a km)	Rs 11.70 (Rs 58.50 a km)
The first kilometer in all	Rs 53	Rs 79.50
Waiting	Rs 7.80 for 2 minutes	Rs 11.70 for 2 minutes

So by day, with distance d km and waiting t minutes,
$$\text{fare} = 14 + 39d + 3.90t$$
and at night every rate is 50% more: 21 + 58.50d + 5.85t.

Fares change. In April 2026, the Bagmati Province government’s notice in the Nepal Gazette was reported to set Rs 58 to start, Rs 12 for each 200 m by day (Rs 17 at night, 9 PM to 4 AM) and Re 1 a minute for waiting up to 30 minutes. We could not read the Gazette notice itself, so the questions here use the 2075 fares for practice; check the notice before you rely on any of them.

The meter’s readings at 0 m, 200 m, 400 m, … are Rs 14, Rs 21.80, Rs 29.60, …: each is the one before plus Rs 7.80. A list of numbers that goes up by the same amount each time is an arithmetic sequence.

Use the 2075 fares from this section.

Question 1

Question 2

Question 3

Find the fare in each case.

	Distance	Time	Waiting
a.	6 km	8 AM	15 minutes
b.	15 km	3:30 PM	10 minutes
c.	7.5 km	11 PM	none
d.	8.75 km	4 AM	7 minutes

Question 4

Question 5

Question 1

Question 2

Question 3

An organization pays income tax of 2.5% on income up to Rs 10 lakh, 4% above Rs 10 lakh up to Rs 20 lakh, 5.25% above Rs 20 lakh up to Rs 40 lakh, and 12.75% above Rs 40 lakh. Find the tax on these yearly incomes.

Question 4

Question 5

A shopkeeper bought a bicycle for Rs 7,520 and sold it at its marked price of Rs 10,000, with 13% VAT.

Question 6

Question 7

Question 8

A dealer bought a computer from an importer for Rs 22,600 with VAT. Adding transport and profit, the dealer sold it to a retailer for Rs 25,990 with VAT, and the retailer sold it to a customer for Rs 28,250 with VAT. VAT is 13%.

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

A 5 A meter is fixed in a house. Its readings, taken on the last day of each month, are:

Month	Baishakh	Jestha	Ashar	Shrawan	Bhadra	Ashoj
Reading	1577	1622	1647	1662	1689	1731

Question 16

Question 17

The first 175 calls cost Rs 200 and each call after that Re 1. Find the total with 13% TSC and 13% VAT for:

Question 18

At the same rates, with 13% TSC and 13% VAT, how many calls were made if the total was:

Question 19

A day taxi meter starts at Rs 14 and adds Rs 7.80 for each 200 m. Find the fare, with no waiting, for:

Grade 9’s final exam is set to CDC’s specification grid for Compulsory Mathematics, Grades 9–10. There, Arithmetic is 13 marks in three questions; the household arithmetic question is usually 4 marks, all about one setting:

Part	Level	Marks	What it asks
a.	understanding	1	a taxi fare from its rates
b.	application	2	a water (or electricity) bill from the tariff table
c.	higher ability	1	worked backwards: the most calls a telephone bill allows

Here is one in that shape, with how it is marked.