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4. पानी प्रशोधन गर्ने एउटा उद्योगमा [tex]$3^{\prime \prime}$[/tex] को पाइपबाट पानी आउने गर्दछ। पानीको व्यवसाय गर्ने व्यक्तिले व्यापारिक सञ्चारका लागि एउटा टेलिफोन सेटसमेत जडान गरेका छन्। उनी आफ्नो घरबाट 12 किलोमिटर टाढा रहेको उक्त पानी उद्योगमा आउन जानका लागि ट्याक्सीको प्रयोग गर्छन्। तलको नियममा आधारित रहेर दिइएका प्रश्नको उत्तर दिनुहोस्:

A water treatment plant receives water through a [tex]$3^{\prime \prime}$[/tex] pipe. A water business person has also installed a telephone set for business communication. He uses a taxi to come and go to the water plant, which is [tex][tex]$12 \text{ km}$[/tex][/tex] from his home. Answer the given questions based on the rules below.

\begin{tabular}{|c|c|c|c|c|}
\hline
\begin{tabular}{l}
ट्याक्सी भाडाको दर \\
(Taxi fare rate)
\end{tabular} & \multicolumn{3}{|c|}{\begin{tabular}{l}
पानीको पाइप (3") प्रतिमहिनाको दर \\
(Per month rate of water pipe (3"))
\end{tabular}} & \begin{tabular}{l}
टेलिफोन महसुल दर \\
(Telephone charge rate)
\end{tabular} \\
\hline
\multirow{3}{}{\begin{tabular}{l}
ट्याक्सी चढ्ने बित्तिकै लाग्ने \\
शुल्क रु. 14 त्यसपछि प्रति \\
किलोमिटरको थप शुल्क रु. 39 \\
(Rs 14 appears in the taxi- \\
metre immediately then \\
the fare of [tex]$1 \text{ km}$[/tex] is Rs 39)
\end{tabular}} & \begin{tabular}{l}
न्यूनतम उपयोग \\
(लिटरमा) \\
(Minimum consumption \\
of water (in liters))
\end{tabular} & \begin{tabular}{l}
न्यूनतम कायम \\
गरिएको मूल्य \\
(रु.) \\
(Minimum \\
charge (Rs))
\end{tabular} & \begin{tabular}{l}
न्यूनतम भन्दा बढी पानी \\
प्रयोग हुँदा प्रति 1 युनिटको थप शुल्क (रु.) \\
(Extra consumption \\
rate per 1 unit (Rs))
\end{tabular} & \multirow{3}{}{\begin{tabular}{l}
पहिलो 175 कलको न्यूनतम \\
शुल्क रु. 200 त्यसपछि प्रति \\
कलको थप शुल्क रु. 1 \\
(The minimum charge of \\
first 175 telephone calls is \\
Rs 200 then the charge of \\
each extra call is Re 1.)
\end{tabular}} \\
\hline
& \begin{tabular}{l}
[tex]$8,81,000$[/tex] \\
लिटर (liters) \\
([tex]$1 \text{ unit} = 1000 \text{ liters}$[/tex])
\end{tabular} & 62,240 & 71 & \\
\hline
& ([tex][tex]$1 \text{ unit} = 1000 \text{ liters}$[/tex][/tex]) & & & \\
\hline
\end{tabular}

(a) घरबाट पानी प्रशोधन गर्ने उद्योगमा एकतर्फ जाँदा मात्र दैनिक उक्त व्यवसायीले ट्याक्सी प्रयोगबापत कति रुियाँ तिर्नुपर्छ?
How much does the businessman have to pay for using a taxi every day when he goes to the water treatment industry from home one way only?
[tex]\[ [1U] \][/tex]
Ans: Rs 482

(b) एक महिनामा [tex]$15,00,000$[/tex] लिटर पानी प्रयोग गरेको उक्त कम्पनीले खानेपानी महसुलवापत कति रुपियाँ बुकाउनु पर्छ?
How much should be paid by the company for water tariff, which used [tex]$15,00,000$[/tex] liters of water in a month?
[tex]\[ [2 A] \][/tex]
Ans: Rs 106189

(c) टेलिफोन खर्च रु. 1000 नबढाउने गरी फोन कल गर्दा उसले एक महिनामा अधिकतम कति कल गर्न सक्छ, गणना गरी उल्लेख गर्नुहोस्।
Calculate and state the maximum number of phone calls he can make in a month not exceeding the telephone expense Rs 1,000
[tex]\[ [1HA] \][/tex]
Ans: 975 calls



Answer :

GinnyAnswer
Let's solve the given problems step-by-step with clear explanations for each part.

### (a) Taxi Fare for One-way Daily Travel

The businessman uses a taxi to travel from home to the water treatment industry, which is 12 kilometers away. The taxi fare structure is:
- An initial charge of Rs. 14
- An additional charge of Rs. 39 per kilometer

To find the total fare for a one-way trip, we calculate as follows:
1. Initial charge: Rs 14
2. Additional charge for 12 km: [tex]\( 12 \, km \times Rs. 39 \, per \, km = Rs. 468 \)[/tex]

Total fare [tex]\( = Rs. 14 + Rs. 468 = Rs. 482 \)[/tex]

### (b) Water Tariff for Monthly Usage

The company uses 15,00,000 liters of water in a month. The water tariff structure is:
- Minimum consumption: 8,81,000 liters
- Minimum charge for this consumption: Rs. 62,240
- Additional charge for consumption beyond the minimum: Rs. 71 per 1,000 liters (1 unit)

To find the total water charges:
1. Calculate the excess water usage:
[tex]\[ 15,00,000 \, liters - 8,81,000 \, liters = 6,19,000 \, liters \][/tex]

2. Convert excess usage into units:
[tex]\[ 6,19,000 \, liters \div 1,000 = 619 \, units \][/tex]

3. Calculate the additional charge for excess usage:
[tex]\[ 619 \, units \times Rs. 71 \, per \, unit = Rs. 43,949 \][/tex]

Total water charges [tex]\( = Rs. 62,240 + Rs. 43,949 = Rs. 1,06,189 \)[/tex]

### (c) Maximum Number of Phone Calls within Rs. 1000 Budget

The businessman can make phone calls with the following rate structure:
- Minimum charge for the first 175 calls: Rs. 200
- Additional charge for each call beyond the first 175: Rs. 1 per call

To find the maximum number of calls within a Rs. 1000 budget:
1. Calculate the remaining budget after the minimum charge:
[tex]\[ Rs. 1000 - Rs. 200 = Rs. 800 \][/tex]

2. Calculate the number of additional calls that can be made with the remaining budget:
[tex]\[ Rs. 800 \div Rs. 1 \, per \, call = 800 \, calls \][/tex]

3. Add the initial 175 calls to the additional calls:
[tex]\[ 175 \, calls + 800 \, calls = 975 \, calls \][/tex]

In conclusion:

(a) The daily one-way taxi fare is Rs. 482.

(b) The total water tariff for the month's usage is Rs. 1,06,189.

(c) The maximum number of phone calls that can be made within a Rs. 1000 budget is 975 calls.

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