Subject: Compulsory Maths

Home arithmetic is simply the arithmetic that is used for the services used in our daily life.

We carry different economic activities within our home too such as payment of electricity bill, water bill, telephone bill, etc. Currently, we can find such bills using the information and communication technology (ICT). For example, bill of public switched telephone network can be found by dialing1601.

Electricity Bill

Nepal Electricity Authority (NEA) charges the bill of electricity that public uses at their home. Bills are charged accordance to a capacity of meter used and a number of units consumes monthly. The NEA meters used in our home are from 220 volts to 400 volts.

Electricity charge as per the rule of electricity

authority:

Capacity of meter |
Unit consumed |
Amount |

5 Ampere | upto 20 | Rs 80 |

6 to 15 Ampere | upto 50 | Rs 365 |

16 to 30 Ampere | upto 100 | Rs 795 |

31 to 60 Ampere | upto 200 | Rs 1765 |

Energy cost as of 2071/72

Rs. 80 at the rate of Rs. 4 per unit up to 50 units

Rs. 7.30 per unit from 50 to 150 units

Rs. 9.50 per unit 150 to 250 units

Rs. 11.00 above 251

**Some of the important information to the electricity consumer:**

- If the meter reader cannot read the meter for three times then, NEA can disconnect the electricity supply at any time.
- The middle number of the consumer ID denotes the day of meter reading.
- If the bill is paid within 7 days of reading, 3% discount is given to consumers.
- The bill is to be paid within 22 days of billing.
- It the bill is paid within 23 to 30 days of billing 5% charge is added.
- It the bill is paid within 31 to 40 days of billing 10% charge is added.
- It the bill is paid within 41 to 60 days of billing 25% charge is added.
- If the bill is not paid until the 60 days of billing, the electric can be disconnected at any time by NEA authorities without any prior notice.

Water consumption is measured in terms of units. The unit of water consumed is measured by Flow meter. Nepal Water supply corporation (NWSC) sends the water bill every month. In Kathmandu Upatekya Khanepani Limited (KUKL) sends the water bill every month to its consumer.According to Nepal Water Supply Corporation, Tariff provided to all branch are as follow:

According to Nepal Water Supply Corporation, Tariff provided to all branch are as follow:

Pipe size (inch) | Minimum consumption (litre) | Minimum cost (Rs.) with meter | For more consumption cost per unit (Rs.) with meter | Main tap charge (Rs) without meter | Branch tap charge (Rs) without tap |

1/2" | 10 units | 110 | 25 | 560 | 200 |

3/4" | 27 units | 1490 | 40 | 3360 | 1600 |

1" | 56 units | 3420 | 40 | 9200 | 2700 |

1.5" | 155 units | 9600 | 40 | 20700 | 6500 |

2" | 320 units | 21600 | 40 | 42300 | 12000 |

3" | 881 units | 49500 | 40 | 131400 | 33000 |

4" | 1810 units | 97200 | 40 | 250200 | 62000 |

1 units mean 1000 litre of water consumption.

50% of water cost is charged a sewerage service charge.

The cost of telephone depends upon the number of calls that we make. Telephone company records the number of calls within their database system. Nepal Telecom Company (NTC) records the telephone bill and we should pay it monthly.

Telephone charge rate as per the rule of Nepal Telecom(NTC).

Rs.200 for a minimum of 175 calls Rs.1 per call above the minimum call.

Call charge = minimum call charge (C) + additional no. of calls (n) * addtional call rate (r)

i.e. call charge = C+n*r

Telecome service charge (TSC) = 10% of call charge

Value added tax (VAT) = (C + TSC)* 13%

Total amount = Call charge (C) + TSC + VAT

According to the certain rule imposed by government authority, the taxi fare is charged. The meters of taxi are provided and regulated by Department of Transport Management together with Nepal Bureau of Standard and Metrology (NBSM).

According to the current rule, the taxi users should pay the bill as mentioned below:

Time | Minimum fare | Rate per 200 m distance |

Morning 6:00 am to Evening 9:00 pm | Rs. 14 | Rs. 7.20 |

Evening 9:00 pm to Morning 6:00 am | Rs.21 | Rs. 10.80 |

- Source: Department of Transport Management

Nepal Bureau of Standard and Metrology

- Home arithmetic is mainly used in our daily life for our household purpose.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

In a house, the electricity meter reading on Chaitra 30 was 1050 units and on Baisakh 30, it was found to be 1250 units.What is the charge to be paid if the rates of charge are as follows?

Minimum charge up to 20 units =Rs.80,

Per units charges (up to 21-250 units) =Rs.7.30

Here, Consumed units of Baisakh=(1250-1050)=200 units

Consumed units of Baisakh=(1250-1050)=200 units

Minimum charge up to 20 units= Rs.80

Additional units =(200-20)=180 units

Charged of additional units =180× Rs.7.30 = Rs 1314

∴Total charge = Rs. 80 + Rs 1314

= Rs.1394 Ans

In a house with 15A electricity transmission line the meter reading on the last day of Ashadh was 2500 units and that of Shrawan eas 2700 units, what is the amount to be paid as per the following rate?[Minimum charge (up to 50 units) Rs.299, above it per unit Rs..30]

Here,

Consumption of electricity in Shrawan =2700-2500=200

Minimumcharge for first 50 units =Rs.299

Now, remaining units =200-50=150

Charges of remaining units =150×Rs.7.30 = RS 1095

∴Total charge =Rs. 299 + Rs 1095

= Rs. 1394. Ans.

A house owner pays to the electricity authority Rs.160 up to 40 units; Rs. 5 per units for the additional units and receives RS.6 per units (using sub-meter)from the person living in rent. He uses 40 units only out of the total 225 units each month.In this condition

- How much charge is paid by the house owner to the electricity authority?
- What amount does the house owner collect from the person living in the rented rooms?
- What is the profit made by the house owner from electricity by giving the house in rent?
- At what rate per unit he has to sell the electricity in order to use 60 units by himself free of cost?

- Here,

By the rule of electricity authority, charges for up to 40 units is Rs.160 and charge for per additional unit is Rs 5.Here 225 units of electricity was consumed.

or, 224 units =40 units + 185 units

Here, charge for first 40 units = Rs.160 and charge for 185 units

185× 5=Rs 925.

Hence, the house owner should pay to electricity authority

Rs(160+925)=Rs.1085 Ans

- Here, House owner uses only 40 units of electricity out of total 225 units each month and collect the charge of remaining (225-40)=185 units from the person living in rent.

∴ He receives for 185 units at the rate of Rs.6 per unit from the person living in rent.

∴ Total charge received from the person living in rent = Rs 6 × 185

= Rs.1110 Ans.

- Here, House of the owner pays the charge Rs. 160 for up to 40 units.

Again, he pays for additional 185 units at the rate of Rs.5 per unit to the electricity authority.

∴ Charge for 185 units = 185× Rs.5=Rs. 925

Total charge to be paid =Rs.160 + Rs 925=Rs.1085

Charge for 185 units received from the person living in rent=Rs.1110

∴Profit made by the house owner =Rs.1110-Rs.1085

= Rs.25 Ans.

- Here, The house owner consumed 60 units by himself and remaining 225-60=165 units are consumed by the person living in rent.

According to above (i) total amount of bill to be paid by the house owner to the electricity authority is Rs.1085

To consume 60 units free of cost bt house owner, he has to receive Rs. 1085 from 165 units.

Here, S.P of 165 = Rs.1085

∴S.P of 1 unit =\(\frac{Rs. 1085}{165}\)

= Rs.6.58.Ans.

The units charged for the electricity is Rs. 7.30 per unit, find the charge to be paid for using a bulb of 60 watts using it for 7 hours 30 minutes. Likewise, what is the total bill for a month of heater of 2000 watts using it for 2 hours 15 minutes daily?

Here,60 watt=\(\frac{60}{1000}\) kw=0.06 kw

7hrs.30 min = 7 hrs + \(\frac{30}{60}\)hrs

=7 \(\frac{1}{2}\)

=\(\frac{15}{2}\)hrs.

Hence, total consumed units in 7 hrs.30 mins =0.06 ×\(\frac{15}{2}\)= 0.45 units.

Now, charge for 0.45 units at the rate of Rs.7.30 per unit =0.45× 7.30=Rs 3.285

∴Total charge to be paid for using a bulb of 60 w of 7 hours 30 minutes =Rs 3.285 Ans.

Again,2000w=\(\frac{2000}{1000}\)=2 kw

2 hours 15 minutes =2 hrs +\(\frac{15}{60}\)hrs.=2 hrs + 0.25 hrs =2.25 hrs.

Total consumed units from 2000 of heater = 2.25× 2 =4.5 units.

Now, Daily charges for 4.5 units at the rate of Rs.7.30

=Rs.(4.5× 7.30)

= Rs.32.85

Now, Daily charge for 1 month = 32.85× 30=985.5.Ans.

In a house of 30 A electricity transmission line, the electricity meter reading in Baisakh 1 is 1050 units and in Jestha 1 is 1250 units.If the rate of payment is Rs.664 up to 100 units and above it Rs.7.35 per unit, how much is to be paid for the electricity charge for the months of Baisakh?

- How many units can be consumed at the same rate for Rs.1058?

Here, Consumption of electricity in Baisakh = 1250-1050=200 units

Charge for first 100 units =Rs.664

Remaining units=200-100=100

Charge for remaining units=100 × Rs. 7.35 =Rs.735

Total charge = Rs.664 + Rs.735 =Rs.1399

- First 100 units can be consumed for Rs.644.

Now, remaining amount =Rs.1058 - Rs Rs.644=Rs.394

Here,for Rs. 7.35 = 1 unit can be consumed

for Rs.1 = \(\frac{1}{7.35}\) unit can be consumed.

for Rs.394=\(\frac{1}{7.35}\)×394 unit can be consumed.

=53.6 units can be consumed.

∴Total units that can be consumed for Rs.1058

= 100 + 53.6 = 153.6 Units Ans.

The initial reading in the meter taxi in Kathmandu is Rs.7 and Rs. 9 is added to each additional km.How long did a passenger travel if he paid Rs.115 as the taxi fare?

Here, Initial charge for meter taxi = Rs.7

Total fare = Rs.115

Taxi fare for distance travelled=Rs.115 -Rs.7 =Rs. 108

Again,per km fare= Rs.9

Hence, total distance travelled =\(\frac{Rs.108}{Rs.9}\)=12 km

Hence, a passenger can travel 12 km for Rs.115.Ans.

Here, Initial charge for meter taxi = Rs.7

Total fare = Rs.115

Taxi fare for distance travelled=Rs.115 -Rs.7 =Rs. 108

Again,per km fare= Rs.9

Hence, total distance travelled =\(\frac{Rs.108}{Rs.9}\)=12 km

Hence, a passenger can travel 12 km for Rs.115.Ans.

If 10 Japanese Yen is equal to Rs.6.34, convert Rs. 22484.81 into Japanese Yen?

Here, N.C 6.34 = 10 Japanese Yen

N.C =\(\frac{10}{6.34}\) Ja panese Yen

∴N.C. 22484.81=\(\frac{10}{6.34}\)×22484.81=35465 Japanese Yen Ans.

It costs Rs.25 I.C. in India, US $6.82 in America and £ 3.90 in Britain to travel 25 km by train.Find the average fare in these three countries in Nepali currency?

Here, from the given table,

I.C. 100 = N.C. 160

or,I.C.1 = N.C. \(\frac{160}{100}\)

or, I.C 25=N.C.\(\frac{160}{100}\)×25= N.C.40

Again, $ 1= N.C.Rs 78

∴ $ 6.82=N.C 78 × 6.82 =N.C.531.96

£ 1 = N.C.121.41

£ 3.9 =N.C. 121.41× 3.9 = N.C. 473.499

Hence, average fare of these three countries in Nepali currency

\(\frac{40+531.96)+473.499}{3}\)

Rs.348.48 Ans.

It costs £604 for the London-Kathmandu-London two-way travel ticket in London , while it costs only Rs.70225 for an air ticket for two-way travel from Kathmandu-London-Kathmandu.Which is cheaper and by what percent?(Exchange rate=Rs.121.41)

Here, Air ticket from Ktm-London-Ktm=Rs 70225

Air ticket from London-Ktm-London =£ 604 =Rs. 604× 121.41

= Rs 73331.64

In Nepal, the air ticket is cheaper by

Rs. 7331.64 - Rs.70225 =Rs.3106

In percent, the ticket in Nepal is cheaper by

=\(\frac{3106}{70225}\)×100

=4.4229

=4.42% Ans.

What is the profit percent if an article purchased for $1 is sold for £1?[$1=Rs. 78 and £1 =Rs. 121.41]

Here, C.P $ 1= Rs.78, S.P =£ 1=Rs.121.41

Actual profit =S.P -C.P=Rs.(121.41-78)

= Rs.43.41

Percentage of profit= \(\frac{Actualprofit}{C.P}\) × 100%

=\(\frac{43.41}{78}\)× 100%

=55.65% Ans.

If Japanese Yen 10=Rs.6.28, convert Rs.35800 to Japanese Yen.

Here, using chain rule,

Japanese Yen 10 =N.C.6.28

N.C. 35800=Japanese Yen x(say)

Here,10× 35800 = 6.28× x

∴ x=\(\frac{10× 35800}{6.28}\)

= 57006.37

Hence, N.C. 35800=Japanese Yen 57006.37 Ans.

If £ 15 = $ 20 and $ 5 = Rs. 390,find the number of pounds that can be exchange for Rs.31200.

Here, Let,£

Let,£ x can be exchange for Rs. 31200

∴£x=Rs.31200.

Rs.390 = $ 5

$20=£15

Now, using chain rule,

x× 390× 20 =31200× 5× 15

∴ x= \(\frac{31200×5×15}{390× 20}\)

= 300

Hence, number of pounds that can be exchanged forRs.31200 is£300.Ans.

If $1=Rs.78 and £1=Rs.117, convert $55 to Pound Sterling.

Here,

Let, $ 55 =£x

Then,£x=$55

$1 =Rs.78

Rs.117 =£1

Now, x×1×117 =55× 78× 1

∴x=\(\frac{55×78×1}{1×117}\)

=36.67

∴$55=£36.67 Ans.

Using the selling rate, convert the following:

- How many US $ could be exchanged for Rs.70250?

Here, Rs. 78.59 = $1

or,Rs,1=$\(\frac{1}{78.59}\)

or, Rs. 70250 =$\(\frac{1}{78.59}\)×70250

= $ 893.88 Ans.

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