G8_Unitary method

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ऐकिक नियम (Unitary Method)

अंकगणितमा Unitary Method भनेको big idea हो। Unitary Method सँग सम्बन्धित विद्यालयका पाठ्यक्रमहरूले तीनचटा मुख्य कुराहरू: भिन्न, अनुपात, र प्रतिशत समेटेको हुन्छ।

1. पहिलो कुरा, Unitary Method ले धेरै समस्याहरूलाई mental algorithms रूपमा हल गर्न मद्दत गर्छ र यो mental arithmetic को महत्वपूर्ण भाग हो। यसलाई एकपटक राम्रोसँग बुझिसकेपछि, दैनिक जीवनका बिविध परिस्थितिहरूमा छिटो र सहज रूपमा समस्या समाधान गर्न सकिन्छ।
2. दोस्रो, Unitary Method मा दक्षता हासिल गर्नुले भिन्न, अनुपात, र प्रतिशत संख्याको संरचनालाई राम्रोसँग बुझ्न मद्दत गर्छ, जसमा अंश (numerator) र हर (denominator) र यस्तै बिभिन्न रुपको को स्पष्ट सम्बन्ध हुन्छ।

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THE BASICS of UNITARY METHOD

Although unitary method is a mental algorithm, it should be taught using three successive parallel sentences. The first sentence restates the problem, and the last states its solution. For example

If 4 mangoes cost 120, how much do 9 mangoes cost?

	4	mangoes cost	=120
÷ 4	1	mango costs	\(=\dfrac{120}{4}=30\)
× 9	9	mangoes cost	\(=30 \times 9=270\)

The method relies on a sequence of parallel sentences. Once the method is mastered, the successive sentences in easier examples can merely be spoken or thought.

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Definition

The method of first finding the value of one article/unit and then, finding the value of more articles/units is called Unitary Method.

In Unitary Method, we use three types of proportions.

1. Direct Proportion (सीधा अनुपात)
   दुईवटा परिमाणहरु मध्ये यदि एक परिमाण बढदा/घट्दा, अर्को परिमाण पनि समानुपातिक रूपमा बढ्छ/घट्छ भने त्यस्तो परिमाणहरुलाई Direct Proportion भनिन्छ। जस्तै बस्तुको सङ्ख्या बढाइयो भने, लाग्ने मुल्य पनि बढ्छ। त्यसैले बस्तुको सङ्ख्या र मुल्य Direct Proportion भएको परिमाणहरु हुन्।

   Weight (kg) \(\uparrow\)	Cost (Rs.) \(\uparrow\)
   10	2,750
   15	x

   The ratio is
   \(\dfrac{x}{2750} =\dfrac{15}{10} \)
   
   
2. Inverse Proportion (प्रतिलोम अनुपात)
   दुईवटा परिमाणहरु मध्ये यदि एक परिमाण बढदा/घट्दा, अर्को परिमाण पनि समानुपातिक रूपमा घट्छ/बढ्छ भने त्यस्तो परिमाणहरुलाई Indirect Proportion भनिन्छ। जस्तै एउटा कार्य गर्नका लागि ५ जना मजदुर लाग्छ र उनीहरूले १० दिन मा काम पूरा गर्छन्। यदि मजदुरहरूको सङ्ख्या दोब्बर (१० जना) गरियो भने, सोही कार्य सम्पन्न गर्न लाग्ने समय घट्छ। त्यसैले कामदारको सङ्ख्या र कार्य सम्पन्न गर्न लाग्ने समय Indirect Proportion भएको परिमाणहरु हुन्।

   People\(\uparrow\)	Days\(\downarrow\)
   5	10
   10	x

   The ratio is
   \(\dfrac{x}{10} =\dfrac{5}{10} \)
   
   
3. Chain Rule (शृंखला नियम)
   Chain Rule भनेको UNITARY METHOD को विस्तारित रुप हो जसले धेरै परिमाणहरू आपसमा सम्बन्धित गर्छ। जस्तै यदि A ले कुनै काम १० दिनमा गर्छ, B ले सोही काम २० दिनमा गर्छ, र C ले ३० दिनमा गर्छ भने, A, B, र C मिलेर काम गर्दा कति दिन लाग्छ?

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Drag and Drop Quiz: Q1

बायाँबाट आइटमहरू तान्नुहोस् र तिनीहरूको सही अनुपात प्रकार वा परिभाषामा राख्नुहोस्:

\(\text{Cost} \uparrow \implies \text{Quantity} \uparrow\)

\(\text{Workers} \uparrow \implies \text{Days} \downarrow\)

\(\text{Ratio} \ \frac{A}{B} = k \ (\text{Constant})\)

\(\text{Distance} \uparrow \implies \text{Fuel Used} \uparrow\)

\(\text{Speed} \uparrow \implies \text{Time Taken} \downarrow\)

\(\text{Workers} \times \text{Days} = k\)

\(\text{Weight} \uparrow \implies \text{Cost} \uparrow\)

\(\text{Pipe Diameter} \uparrow \implies \text{Filling Time} \downarrow\)

सीधा अनुपात (Direct Proportion)

प्रतिलोम अनुपात (Inverse Proportion)

सीधा अनुपात सूत्र (Direct Formula)

सीधा अनुपात उदाहरण

प्रतिलोम अनुपात उदाहरण

प्रतिलोम अनुपात सूत्र (Inverse Formula)

सीधा अनुपात उदाहरण

प्रतिलोम अनुपात उदाहरण

Score: 0/10

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Multiple Choice Quiz1: Try it

Question 1 of 5

Question text will appear here

Quiz Complete! Your Score: 0/5

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Questions

1. १५ जना कामदारले एउटा काम २५ दिनमा सक्छन् भने कति कामदार थप्दा सो काम १५ दिनमा सकिन्छ? 15 workers can do a piece of work in 25 days. How many workers should be added to complete the same work in 15 days?
Given that

People\(\uparrow\)	Days\(\downarrow\)
15	25
15+x	15
We know that "number of people" and "number of days" to complete a work have indirect relation (more people → less days), therefore, using the relation indirect relation, we get
\(\dfrac{15+x}{15} =\dfrac{25}{15} \)

or\(15+x=25\)

or\(x=10\)

Thus, 10 more workers should be added to complete the same work in 15 days
2. १० kg स्याउको मूल्य रु. २,७५० पर्छ भने १५ kg स्याउको मूल्य कति पर्ला? If the cost of 10 kg of apples is Rs. 2,750, what will be the cost of 15 kg of apples?
Given that

Weight (kg) \(\uparrow\)	Cost (Rs.) \(\uparrow\)
10	2,750
15	x
We know that weight and cost have a direct relation (more weight → more cost), so we use direct proportion:
\(\dfrac{x}{15} = \dfrac{2750}{10}\)

or\(10x = 2750 \times 15\)

or\(x = \dfrac{41,250}{10} = 4,125\)

Thus, the cost of 15 kg of apples is Rs. 4,125
3. यदि रु. ६० मा ५ वोटा कलम पाइन्छ भने रु. २४० मा कतिवटा कलम पाइन्छ, पत्ता लगाउनुहोस्। If 5 pens can be bought for Rs. 60, how many pens can be bought for Rs. 240?
Given that

Amount (Rs.) \(\uparrow\)	Number of pens \(\uparrow\)
60	5
240	x
We know that "amount" and "number of pens" have direct relation (more pen → more cost), therefore, using direct proportion, we get
\(\dfrac{x}{5} = \dfrac{240}{60}\)

or\(60x = 5 \times 240\)

or\(x = \dfrac{1200}{60} = 20\)

Thus, 20 pens can be bought for Rs. 240.
4. ५ kg सन्तराको रु. १,१२५ पर्छ भने १० kg सन्तराको मूल्य पत्ता लगाउनुहोस्। If the cost of 5 kg of oranges is Rs. 1,125, find the cost of 10 kg of oranges?
Given that

Weight (kg) \(\uparrow\)	Cost (Rs.) \(\uparrow\)
5	1,125
10	x
We know that weight and cost have a direct relation (more weight → more cost), therefore, using direct proportion, we get
\(\dfrac{x}{1125} = \dfrac{10}{5}\)

or\(5x = 1125 \times 10\)

or\(x = \dfrac{11,250}{5} = 2,250\)

Thus, the cost of 10 kg of oranges is Rs. 2,250.
5. १० जना मानिसले एउटा काम १५ दिनमा पूरा गर्न सक्छन् भने ५ जना मानिसले उक्त काम कति दिनमा गर्न सक्छन्? पत्ता लगाउनुहोस्। If 10 men can complete a work in 15 days, how long will 5 men take to complete the work? Find it.
Given that

People \(\downarrow\)	Days \(\uparrow\)
10	15
5	x
We know that "number of people" and "number of days" have an indirect relation (fewer people → more days), therefore, using indirect proportion, we get
\(\dfrac{x}{15} = \dfrac{10}{5}\)

or\(x = \dfrac{10}{5} \times 15\)

or\(x = 30\)

Thus, 5 men will take 30 days to complete the same work.
6. यदि २० जना कामदारले कुनै एउटा काम ४८ दिनमा सक्छन् भने कति दिनमा ३० कामदारले सो काम सक्छन्? If 20 workers can complete a work in 48 days, then in how many days 20 workers will complete the same work?
Given that

People \(\uparrow\)	Days \(\downarrow\)
20	48
30	x
We know that "number of people" and "number of days" have an indirect relation (more people → fewer days), therefore, using indirect proportion, we get
\(\dfrac{x}{48} = \dfrac{20}{30}\)

or\(x = \dfrac{20}{30} \times 48\)

or\(x = 32\) days

Thus, 30 workers will complete the work in \(32\) days .
7. ५ kg स्याउ र ३ दर्जन केराको जम्मा मूल्य रु. ९०० छ र २ kg स्याउको मूल्य रु. २४० पर्छ भने ५ दर्जन केराको मूल्य पत्ता लगाउनुहोस्। The cost of 5 kg apples and 3 dozen banana is Rs. 900. If the cost of 2 kg apples is Rs. 240, find the cost of 5 dozen banana.
First, find the cost of 1 kg apple:
Cost of 2 kg apples = Rs. 240

∴ Cost of 1 kg apple = \(\dfrac{240}{2} = 120\)

∴ Cost of 5 kg apples = \(5 \times 120 = 600\)

Given that:
Cost of (5 kg apples + 3 dozen bananas) = Rs. 900

⇒ 600 + cost of 3 dozen bananas = 900

⇒ Cost of 3 dozen bananas = 900 − 600 = 300

⇒ Cost of 1 dozen bananas = \(\dfrac{300}{3} = 100\)

⇒ Cost of 5 dozen bananas = \(5 \times 100 = 500\)

Thus, the cost of 5 dozen bananas is Rs. 500.
8. १२ जना कामदारले कुनै एउटा काम २० दिनमा गर्न सक्छन्। सोही काम १६ दिनमा सक्नका लागि कति जना कामदार थप्नुपर्ला? 12 workers can complete a piece of work in 20 days. How many workers should be added to complete the work in 16 days?
Given that

People \(\uparrow\)	Days \(\downarrow\)
12	20
12 + x	16
We know that "number of people" and "number of days" have an indirect relation (more people → fewer days), therefore, using indirect proportion, we get
\(\dfrac{12 + x}{12} = \dfrac{20}{16}\)

or\(12 + x = 15\)

or\(x = 3\)

Thus, 3 more workers should be added to complete the work in 16 days.
9. १५ जना कामदारले १० घण्टा प्रतिदिन काम गरी ३० दिनमा पूरा गरे। २५ दिनमा काम पूरा गर्न प्रतिदिन कति घण्टाका दरले काम गर्नुपर्ला? 15 workers can complete a piece of work in 30 days working 10 hours per day. How many hours per day must he work to complete the work in 25 days?
Given that

Days \(\downarrow\)	Hours per day \(\uparrow\)
30	10
25	x
(Number of workers remains the same, so we compare only days and hours per day.)
We know that "number of days" and "hours per day" have an indirect relation (fewer days → more hours per day), therefore, using indirect proportion, we get
\(\dfrac{x}{10} = \dfrac{30}{25}\)

or\(x = 10 \times \dfrac{30}{25}\)

or\(x = 12\)

Thus, they must work 12 hours per day to complete the work in 25 days.
10. १५ जना मानिसले कुनै काम ४० दिनमा गर्न सक्छन्। यदि ५ जना मानिस घटाउँदा सो काम कति दिनमा सकिएला? 15 men can do a piece of work in 80 days. How long will it take to complete the work if 5 men are reduced?
Given that

People \(\downarrow\)	Days \(\uparrow\)
15	80
15 − 5 = 10	x
We know that "number of people" and "number of days" have an indirect relation (fewer people → more days), therefore, using indirect proportion, we get
\(\dfrac{x}{80} = \dfrac{15}{10}\)

or\(x = \dfrac{15}{10} \times 80\)

or\(x = 120\)

Thus, the work will be completed in 120 days if 5 men are reduced.
11. १८ जना कामदारले एउटै काम ९१ दिनमा गर्न सक्छन् भने ३ जना कामदार थप्दा सो काम कति दिनमा सकिएला? 18 workers can do a piece of work in 91 days. How long will it take to complete the work if 3 workers are added?
Given that

People \(\downarrow\)	Days \(\uparrow\)
18	31
18 + 3 = 21	x
We know that "number of people" and "number of days" have an indirect relation (fewer people → more days), therefore, using indirect proportion, we get
\(\dfrac{x}{91} = \dfrac{21}{15}\)

or\(x = \dfrac{21}{15} \times 91\)

or\(x = 78\)

Thus, the work will be completed in 78 days if 3 workers are added.
12. कुनै एक टुक्रा जमिनको \(\frac{१}{३}\) भागको मूल्य रु. ३,६४० पर्छ भने पूरै जमिनको मूल्य कति पर्छ? त्यसै ४ टुक्राको मूल्य कति पर्ला? [Ans: रु. 7,840] If \(\frac{१}{३}\) of a piece of land is cost Rs. 3,540, what is the cost of the whole land? What is the cost of such 4 pieces?
Given that
Cost of \(\dfrac{1}{4}\) of land = Rs. 3,540

orCost of whole land = \(4 \times 3,540 = 14,160\)

orCost of 4 such whole pieces = \(4 \times 14,160 = 56,640\)

Thus, the cost of the whole land is Rs. 14,160 and the cost of 4 such pieces is Rs. 56,640.
13. ४ दर्जन सिसाकलमको मूल्य रु. २६४ पर्छ भने ५० वटा सिसाकलमको मूल्य कति पर्ला? If the price of 4 dozen pencils is Rs. 264, what will be the price of 50 pencils?
Given that
4 dozen pencils = 4 × 12 = 48 pencils


Number of pencils \(\uparrow\)	Cost (Rs.) \(\uparrow\)
48	264
50	x
We know that number of pencils and cost have a direct relation, therefore, using direct proportion, we get
\(\dfrac{x}{264} = \dfrac{50}{48}\)

or\(x = \dfrac{50}{48} \times 264\)

or\(x = 275\)

Thus, the price of 50 pencils is Rs. 275.
14. यदि ४० kg धानको मूल्य रु. २,५०० भए एक क्विन्टल धानको मूल्य पत्ता लगाउनुहोस्। If the cost of 40 kg rice is Rs. 2,500, find the cost of one quintal rice.
We know that:
1 quintal = 100 kg

Given that

Weight (kg) \(\uparrow\)	Cost (Rs.) \(\uparrow\)
40	2,500
100	x
Since weight and cost have a direct relation, using direct proportion, we get
\(\dfrac{x}{2500} = \dfrac{100}{40}\)

or\(x = \dfrac{100}{40} \times 2500\)

or\(x = 6,250\)

Thus, the cost of one quintal (100 kg) rice is Rs. 6,250.
15. यदि ३० वटा सुन्तलाको मूल्य रु. १८० भए २ दर्जन सुन्तलाको मूल्य पत्ता लगाउनुहोस्। [Ans: रु. 144] If the cost of 30 oranges is Rs. 180, find the cost of 2 dozen oranges.
First, note that:
2 dozen oranges = 2 × 12 = 24 oranges

Given that

Number of oranges \(\uparrow\)	Cost (Rs.) \(\uparrow\)
30	180
24	x
Since number of oranges and cost have a direct relation, using direct proportion, we get
\(\dfrac{x}{180} = \dfrac{24}{30}\)

or\(x = \dfrac{24}{30} \times 180\)

or\(x = 144\)

Thus, the cost of 2 dozen oranges is Rs. 144.
16. ८ वोटा टेबुल र २ वोटा कुर्सीको जम्मा मूल्य रु. १३,००० छ। यदि २ वटा टेबुलको मूल्य रु. २,४०० भए १ वटा कुर्सीको मूल्य पत्ता लगाउनुहोस्। Total cost of 5 tables and 7 chairs is Rs. 19,000. If the cost of 2 tables is Rs. 2,400, find the cost of one chair.
Given that:
Cost of 2 tables = Rs. 2,400

∴ Cost of 1 table = \(\dfrac{2400}{2} = 1,200\)

∴ Cost of 8 tables = \(8 \times 1,200 = 9,600\)

Also given:
Cost of (8 tables + 2 chairs) = Rs. 13,000

⇒ 9,600 + cost of 2 chairs = 13,000

⇒ Cost of 2 chairs = 13,000 − 9,600 = 3,400

⇒ Cost of 1 chair = \(\dfrac{3,400}{2} = 1,700\)

Thus, the cost of one chair is Rs. 1,700.
17. एउटा बसलाई ७५ km दूरी पार गर्न १५ लिटर डिजेल चाहिन्छ। २०० लिटर डिजेलले कति km दूरी पार गर्न सक्ला? A bus needs 15 litres of diesel to travel 75 km of distance. How many kilometers will it travel on 200 litres of diesel?
Given that

Diesel (litres) \(\uparrow\)	Distance (km) \(\uparrow\)
15	75
200	x
We know that diesel and distance have a direct relation (more diesel → more distance), therefore, using direct proportion, we get
\(\dfrac{x}{75} = \dfrac{200}{15}\)

or\(x = \dfrac{200}{15} \times 75\)

or\(x = 1,000\)

Thus, the bus will travel 1,000 km on 200 litres of diesel.
18. अनुजाले ४ km/hr को गतिमा साइकल चलाउँदा ७०० मिटर दूरी पार गर्न कति समय लाग्ला? How long will Anuja take to cover 700 meters of distance when she rides a bicycle at the speed of 4 km/hr?
Given:
Speed = 4 km/hr
Distance = 700 metres = \(\dfrac{700}{1000} = 0.7\) km

We know that:
Time = \(\dfrac{\text{Distance}}{\text{Speed}}\)

Time = \(\dfrac{0.7}{4} = 0.175\) hours

Convert hours into minutes:
0.175 × 60 = 10.5 minutes

or10 minutes 30 seconds

Thus, Anuja will take 10 minutes 30 seconds to cover 700 metres.
19. एउटा होस्टलमा ६०० विद्यार्थीको लागि ५० दिनको पुग्ने खाने रसद छ। १५ दिनपछि, १८० जना विद्यार्थीले होस्टल छोडे भने सो खाने कति दिन पुग्छ होला? A hostel has food for 600 students for 50 days. After 15 days, 180 students leave the hostel. How long will the food last?
Given that

Students \(\uparrow\)	Days \(\downarrow\)
600	50-15
600-180	x
We know that "number of students" and "number of days" have an indirect relation (more people → fewer days), therefore, using indirect proportion, we get
\(\dfrac{x}{35} = \dfrac{600}{420}\)

orx = \(x=\dfrac{35 \times 600}{420} = 50\)

Thus, the remaining food will last for 50 more days.

20. १०० जना सिपाहीलाई ६० दिनलाई पुग्ने रसद छ। यदि १२ दिनपछि, २०० जना सिपाहीहरू उनीहरूसँग थपिए भने सो रसद कति समयसम्म चल्ला? 100 soldiers have provision for 60 days at 60 days. If 200 soldiers join them after 12 days, how long will the remaining provisions last?
Given that

Soldiers \(\uparrow\)	Days \(\downarrow\)
100	60 − 12 = 48
100 + 200 = 300	x
We know that "number of soldiers" and "number of days" have an indirect relation (more soldiers → fewer days), therefore, using indirect proportion, we get
\(\dfrac{x}{48} = \dfrac{100}{300}\)

or\(x = \dfrac{100}{300} \times 48 = 16\)

Thus, the remaining provision will last for 16 more days.

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G8_Profit and Loss_Questions

Questions

1. एउटा मोबाइलको क्रय मूल्य रु. \(21,000\) र अङ्कित मूल्य क्रय मूल्यभन्दा \(30\%\) ले बढी छ । (The cost price of a mobile is Rs. \(21,000\) and the marked price is \(30\%\) above the cost price.)
   1. नाफा प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । (Write the formula to find profit percent.) [1]
   2. अङ्कित मूल्य पत्ता लगाउनुहोस् । (Find the marked price.) [1]
   3. उक्त मोबाइल रु. \(24,024\) मा बेचिएको भए छुट रकम पत्ता लगाउनुहोस् । (If the mobile phone was sold for Rs. \(24,024\), find the discount amount.) [1]
   Answer 1

   1. Formula to find profit percent is
      Profit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
      orProfit Percent = \( \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100\% \)
   2. Finding the marked price
      Cost Price (CP) = Rs. \(21,000\)
      Marked Price is \(30\%\) above CP.
      Therefore
      Marked Price (MP) = 130% of CP
      orMP = \( \dfrac{130}{100} \times 21,000 = 27,300 \)
      So, the marked price is Rs. \(27,300\).
   3. Finding the discount amount
      Selling Price (SP) = Rs. \(24,024\)
      Marked Price (MP) = Rs. \(27,300\)
      Discount= MP – SP
      orDiscount = \(27,300 - 24,024 = 3,276\)
      So, the discount amount is Rs. \(3,276\).
2. रु. \(45,000\) पर्ने एउटा ल्यापटप \(20\%\) छुटमा बेचिएको छ । A laptop costing Rs. \(45,000\) is sold at a discount of \(20\%\).
   1. छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find discount percent. [1K]
   2. छुट रकम पत्ता लगाउनुहोस् । Find the discount amount. [1U]
   3. उक्त ल्यापटप \(10\%\) घाटामा बेचिएको रहेछ भने क्रय मूल्य पत्ता लगाउनुहोस् । If the laptop is sold at a loss of \(10\%\), find the cost price. [2A]
   1. Formula to find discount percent is
      Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
      orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
   2. Finding the discount amount
      Marked Price (MP) = Rs. \(45,000\)
      Discount Percent = \(20\%\)
      Therefore,
      Discount Amount = \(20\%\) of MP
      orDiscount Amount = \( \dfrac{20}{100} \times 45,000 = 9,000 \)
      So, the discount amount is Rs. \(9,000\).
   3. Finding the cost price when sold at \(10\%\) loss
      Selling Price (SP) = Marked Price – Discount = \(45,000 - 9,000 = 36,000\)
      Loss Percent = \(10\%\)
      We know that,
      SP = \(90\%\) of CP
      So,
      \(36,000 = \dfrac{90}{100} \times \text{CP}\)
      or\(\text{CP} = \dfrac{36,000 \times 100}{90} = 40,000\)
      Hence, the cost price of the laptop is Rs. \(40,000\).
3. सन्तरामले अङ्कित मूल्य रु. \(1800\) भएको एउटा पङ्खा \(20\%\) छुटमा किनेछन् । Santaram bought a fan of level price Rs. \(1800\) at \(20\%\) discount.
   1. छुट प्रतिशत (\(D\%\)) र अङ्कित मूल्य (\(MP\)) भएको सामानको विक्रय मूल्य कति हुन्छ ? How much is the selling price of an article whose marked price is \(MP\) and the discount percent is \(D\%\)? [1K]
   2. उक्त पङ्खाको विक्रय मूल्य पत्ता लगाउनुहोस् । Find the selling price of the fan. [1U]
   3. उक्त पङ्खा \(10\%\) नोक्सानमा बेचिएको रहेछ भने क्रय मूल्य पत्ता लगाउनुहोस् । If the fan is sold at \(10\%\) loss, find the cost price. [2A]
1. The selling price (SP) of an article with marked price \(MP\) and discount percent \(D\%\) is given by:
   Selling Price (SP) = \( MP - \dfrac{D}{100} \times MP \)
   orSelling Price (SP) = \( (100-D)\%\times MP \)
2. Finding the selling price of the fan
   Marked Price (MP) = Rs. \(1800\)
   Discount Percent = \(20\%\)
   Therefore,
   \(SP = 80\% \times 1800 =1440\)
   So, the selling price of the fan is Rs. \(1440\).
3. Finding the cost price when sold at \(10\%\) loss
   Selling Price (SP) = Rs. \(1440\)
   Loss Percent = \(10\%\)
   We know that,
   SP = \(90\%\) of CP
   So,
   \(1440 = \dfrac{90}{100} \times \text{CP}\)
   or\(\text{CP} = \dfrac{1440 \times 100}{90} = 1600\)
   Hence, the cost price of the fan is Rs. \(1600\).
4. अङ्कित मूल्य रु. \(25,000\) भएको एउटा मोबाइल \(10\%\) छुटमा बेचिएछ । A mobile set of marked price Rs. \(25,000\) is sold on a discount of \(10\%\).
   1. छुट प्रतिशत (\(D\%\)) र अङ्कित मूल्य (\(MP\)) दिइएको अवस्थामा विक्रय मूल्य (\(SP\)) पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find the selling price (\(SP\)) when discount percent (\(D\%\)) and the marked price (\(MP\)) are given. [1K]
   2. उक्त मोबाइलको विक्रय मूल्य पत्ता लगाउनुहोस् । Find the selling price of the mobile. [1U]
   3. उक्त मोबाइलको क्रय मूल्य रु. \(20,000\) भए नाफा प्रतिशत पत्ता लगाउनुहोस् । If the cost price of the mobile is Rs. \(20,000\), find the profit percent. [2A]
1. The formula to find the selling price (\(SP\)) when marked price (\(MP\)) and discount percent (\(D\%\)) are given is:
   \( SP = MP - \dfrac{D}{100} \times MP \)
   or\( SP = (100-D)\% \times MP \)
2. Finding the selling price of the mobile
   Marked Price (MP) = Rs. \(25,000\)
   Discount Percent = \(10\%\)
   Therefore,
   \( SP = 90\% \times 25,000 = 22,500 \)
   So, the selling price of the mobile is Rs. \(22,500\).
3. Finding the profit percent
   Cost Price (CP) = Rs. \(20,000\)
   Selling Price (SP) = Rs. \(22,500\)
   Profit = SP – CP = \(22,500 - 20,000 = 2,500\)
   Now,
   Profit Percent = \( \dfrac{Profit}{CP} \times 100\% = \dfrac{2,500}{20,000} \times 100\% \)
   orProfit Percent = \(12.5\% \)
   Hence, the profit percent is \(12.5\%\).
5. अङ्कित मूल्य रु. \(750\) भएको एउटा पुस्तक रु. \(600\) मा बेचिएछ । A book with marked price Rs. \(750\) is sold for Rs. \(600\).
   1. छुट प्रतिशत भन्नाले के बुझिन्छ ? लेख्नुहोस् । What is meant by discount percent? Write it. [1K]
   2. छुट प्रतिशत पत्ता लगाउनुहोस् । Find the discount percent. [1U]
   3. उक्त पुस्तक \(13\%\) मूल्य अभिवृद्धि कर (\(VAT\)) लगाएर बेच्दा मूल्य कति पर्छ ? If the book is sold with \(13\%\) value added tax (\(VAT\)), find the price with \(VAT\). [2A]
   1. Discount percent is the percentage of the marked price that is reduced or given as a concession to the customer while selling the article. It is calculated on the marked price (MP).
   2. Finding the discount percent
      Marked Price (MP) = Rs. \(750\)
      Selling Price (SP) = Rs. \(600\)
      Discount Amount = MP – SP = \(750 - 600 = 150\)
      Now,
      Discount Percent = \( \dfrac{Discount}{MP} \times 100\% = \dfrac{150}{750} \times 100\%=20\% \)
      So, the discount percent is \(20\%\).
   3. Finding the price with \(13\%\) VAT
      Selling Price (before VAT) = Rs. \(600\)
      VAT Percent = \(13\%\)
      Proce with VAT = \(113\%\) of \(600 = \dfrac{113}{100} \times 600 = 678\)
      Hence, the price of the book including \(13\%\) VAT is Rs. \(678\).
6. अङ्कित मूल्य रु. \(70,000\) भएको एउटा टेलिभिजन \(20\%\) छुटमा बेचिएछ । A television with marked price Rs. \(70,000\) is sold at a discount of \(20\%\).
   1. विक्रय मूल्य (\(SP\)) लाई अङ्कित मूल्य (\(MP\)) र छुट प्रतिशतको रूपमा लेख्नुहोस् । Write the selling price (\(SP\)) in terms of marked price (\(MP\)) and discount percent. [1K]
   2. उक्त टेलिभिजनको विक्रय मूल्य पत्ता लगाउनुहोस् । Find the selling price. [1U]
   3. उक्त टेलिभिजनमा \(12\%\) नाफा भएको भए क्रयमूल्य पत्ता लगाउनुहोस् । Find the cost price of the television if there is \(12\%\) profit.[2A]
1. The selling price (\(SP\)) in terms of marked price (\(MP\)) and discount percent (\(D\%\)) is:
   \( SP = MP - \dfrac{D}{100} \times MP \)
   or\( SP = (100-D)\% \times MP \)
2. Finding the selling price of the television
   Marked Price (MP) = Rs. \(70,000\)
   Discount Percent = \(20\%\)
   Therefore,
   \( SP = 80\% \times 70,000 =0.8 \times 70,000 = 56,000 \)
   So, the selling price of the television is Rs. \(56,000\).
3. Finding the cost price when profit is \(12\%\)
   Selling Price (SP) = Rs. \(56,000\)
   Profit Percent = \(12\%\)
   We know that,
   SP = \(112\%\) of CP
   So,
   \(56,000 = \dfrac{112}{100} \times \text{CP}\)
   or\(\text{CP} = \dfrac{56,000 \times 100}{112} = 50,000\)
   Hence, the cost price of the television is Rs. \(50,000\).
7. \(20\%\) छुटमा किन्दा एउटा मोटरसाइकलको मूल्य रु. \(1,20,000\) पर्छ । When a motorcycle is sold for \(20\%\) discount, it costs Rs.
   1. छुट प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find the discount percent. [1K]
   2. उक्त मोटरसाइकलको अङ्कित मूल्य पत्ता लगाउनुहोस् । Find the marked price of the motorcycle. [2U]
   3. उक्त मोटरसाइकलको क्रय मूल्य रु. \(1,25,000\) भए नोक्सान प्रतिशत पत्ता लगाउनुहोस् । If the cost price of the motorcycle is Rs. \(1,25,000\), find the loss percent. [2A]
1. The formula to find discount percent is:
   Discount Percent = \( \dfrac{\text{Marked Price} - \text{Selling Price}}{\text{Marked Price}} \times 100\% \)
   orDiscount Percent = \( \dfrac{\text{Discount Amount}}{MP} \times 100\% \)
2. Finding the marked price of the motorcycle
   Selling Price (SP) = Rs. \(1,20,000\)
   Discount Percent = \(20\%\)
   We know that
   SP = \(80\% \times MP\)
   or\(1,20,000 = \dfrac{80}{100} \times MP\)
   or\(MP = \dfrac{1,20,000 \times 100}{80} = 1,50,000\)
   So, the marked price of the motorcycle is Rs. \(1,50,000\).
3. Finding the loss percent
   Cost Price (CP) = Rs. \(1,25,000\)
   Selling Price (SP) = Rs. \(1,20,000\)
   Loss = CP – SP = \(1,25,000 - 1,20,000 = 5,000\)
   Now,
   Loss Percent = \( \dfrac{Loss}{CP} \times 100\% = \dfrac{5,000}{1,25,000} \times 100\% =4\%\)
   Hence, the loss percent is \(4\%\).
8. नयाँ सडकको एउटा पसलमा अङ्कित मूल्य रु. \(40,000\) भएको एउटा मोबाइल सेट रु. \(35,000\) मा बेचिएछ । In a shop in New Road, a mobile set with marked price Rs. \(40,000\) was sold for Rs. \(35,000\).
   1. छुट दिइएको रकम कति रहेछ ? पत्ता लगाउनुहोस् । How much was the discount amount? Find it. [1K]
   2. कति प्रतिशत छुट दिइएको रहेछ ? पत्ता लगाउनुहोस् । What was the percent of discount allowed? Find it. [1U]
   3. \(13\%\) \(VAT\) सहित उक्त मोबाइल रु. \(39,550\) मा बेचिएको रहेछ भने \(VAT\) बिनाको विक्रय मूल्य पत्ता लगाउनुहोस् । Find the selling price of the mobile without \(VAT\) if it was sold for Rs. \(39,550\) with \(13\%\) \(VAT\). [2A]
1. Finding the discount amount
   Marked Price (MP) = Rs. \(40,000\)
   Selling Price (SP) = Rs. \(35,000\)
   Discount Amount = MP – SP = \(40,000 - 35,000 = 5,000\)
   So, the discount amount is Rs. \(5,000\).
2. Finding the discount percent
   Discount Amount = Rs. \(5,000\)
   Marked Price (MP) = Rs. \(40,000\)
   Discount Percent = \( \dfrac{5,000}{40,000} \times 100\% = 12.5\% \)
   So, the discount percent is \(12.5\%\).
3. Finding the selling price without VAT
   Price including VAT (ASP)= Rs. \(39,550\)
   VAT Percent = \(13\%\)
   Let the selling price without VAT be \(SP\).
   Then,
   \(ASP= 113\% \times SP \)
   or\(39500=1.13 \times SP\)
   or\(SP = \dfrac{39,550}{1.13} = 35,000\)
   Hence, the selling price of the mobile without VAT is Rs. \(35,000\).
9. रामलाल एउटा ग्यास चुलो किन्न एउटा पसलमा गएछन् । उसले अङ्कित मूल्य रु. \(4200\) भएको चुलो \(10\%\) छुटमा किनेछन् । Ramlal went to a shop to buy a gas stove. He bought a gas stove at \(10\%\) discount whose marked price was Rs. \(4200\).
   1. छुट प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find discount percent. [1K]
   2. उक्त चुलो किन्दा कति छुट पाएछन् ? How much discount did he get while buying the stove? [1U]
   3. उक्त चुलो बेच्दा पसलेलाई \(5.5\%\) नोक्सान भएको रहेछ भने उक्त चुलोको क्रय मूल्य पत्ता लगाउनुहोस् । While selling that stove the shopkeeper had \(5.5\%\) loss, find the cost price of the stove. [2A]
1. The formula to find discount percent is:
   Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
   orDiscount Percent = \( \dfrac{MP - SP}{MP} \times 100\% \)
2. Finding the discount amount Ramlal received
   Marked Price (MP) = Rs. \(4200\)
   Discount Percent = \(10\%\)
   Discount Amount = \(10\%\) of \(4200 = \dfrac{10}{100} \times 4200 = 420\)
   So, Ramlal got a discount of Rs. \(420\).
3. Finding the cost price of the stove for the shopkeeper
   Selling Price (SP) = MP – Discount = \(4200 - 420 = 3780\)
   Loss Percent = \(5.5\%\)
   We know that,
   SP =\(94.5\%\) of CP
   So,
   \(3780 = \dfrac{94.5}{100} \times \text{CP}\)
   or\(\text{CP} = \dfrac{3780 \times 100}{94.5} = 4000\)
   Hence, the cost price of the stove for the shopkeeper was Rs. \(4000\).
10. राजनले \(14\%\) छुटमा एउटा स्वेटर किन्दा रु. \(1075\) तिरेछन् । Rajan bought a sweater for Rs. \(1075\) at a discount of \(14\%\).
    1. अङ्कित मूल्य र विक्रय मूल्यको अन्तरलाई के भनिन्छ ? What is called the difference between marked price and selling price? [1K]
    2. उक्त स्वेटरको अङ्कित मूल्य पत्ता लगाउनुहोस् । Find the marked price of the sweater. [1U]
    3. उक्त स्वेटर \(7.5\%\) नाफामा बेचिएको रहेछ भने क्रय मूल्य पत्ता लगाउनुहोस् । If the sweater is sold at \(7.5\%\) profit, find the cost price. [2A]
1. The difference between marked price (MP) and selling price (SP) is called the "discount amount".
2. Finding the marked price of the sweater
   Selling Price (SP) = Rs. \(1075\)
   Discount Percent = \(14\%\)
   We know that
   \(SP = 86\%\) of MP
   or\(1075 = \dfrac{86}{100} \times MP\)
   or\(MP = \dfrac{1075 \times 100}{86} = 1250\)
   So, the marked price of the sweater is Rs. \(1250\).
3. Finding the cost price when sold at \(7.5\%\) profit
   Selling Price (SP) = Rs. \(1075\)
   Profit Percent = \(7.5\%\)
   We know that,
   SP = \(107.5\%\) of CP
   So,
   \(1075 = \dfrac{107.5}{100} \times \text{CP}\)
   or\(\text{CP} = \dfrac{1075 \times 100}{107.5} = 1000\)
   Hence, the cost price of the sweater is Rs. \(1000\).
11. सीताले एउटा मोबाइल रु. \(24,000\) मा किनिछन् । उनले \(20\%\) छुटमा उक्त मोबाइल किनिछन्। Sita bought a mobile at Rs. \(24,000\). She has bought at \(20\%\) discount.
    1. छुट प्रतिशत र अङ्कित मूल्य दिइएमा छुट रकम पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find discount amount when discount percent and marked price are given.[1U]
    2. उक्त मोबाइलको अङ्कित मूल्य पत्ता लगाउनुहोस् । Find the marked price of the mobile. [2U]
    3. \(13\%\) भ्याटसहित उक्त मोबाइलको मूल्य कति हुन्छ ? What will be the cost of the mobile with \(13\%\) VAT? [1A]
 
   
     
1. The formula to find the discount amount is:
           Discount Amount = \( D\% \times \text{Marked Price} \)
           orDiscount Amount = \( \dfrac{D}{100} \times MP \)      
     
2. Finding the marked price of the mobile
           Selling Price (SP) = Rs. \(24,000\)
           Discount Percent (\(D\%\)) = \(20\%\)
           We know that,
           SP = 80\%\) of MP
                  or\(24,000 = \dfrac{80}{100} \times MP\)
           or\(MP = \dfrac{24,000 \times 100}{80} = 30,000\)
           So, the marked price of the mobile is Rs. \(30,000\).      
     
3. Finding the cost of the mobile with \(13\%\) VAT
           Selling Price (SP) = Rs. \(24,000\)
           VAT Percent = \(13\%\)
           Price with VAT (ASP) = \(113\%\) of SP
           orASP = \((100+13)\% \times SP\)
           orASP = 1.13 \times 24,000 = 27,120\)
           Hence, the cost of the mobile with \(13\%\) VAT is Rs. \(27,120\).      
   
 
12. अङ्कित मूल्य रु. \(5000\) भएको एउटा साइकल \(5\%\) छुट दिई बेच्दा \(10\%\) नाफा हुन्छ । A cycle whose marked price is Rs. \(5000\) is sold at a discount of \(5\%\) making \(10\%\) profit.
    1. नाफा प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find profit percent. [1K]
    2. छुट रकम र विक्रय मूल्य पत्ता लगाउनुहोस् । Find the discount amount and the selling price. [2U]
    3. क्रय मूल्य पत्ता लगाउनुहोस् । Find the cost price. [1U]
 
   
     
1. The formula to find the profit percent is:
           Profit Percent = \( \dfrac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\% \)
           orProfit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)      
     
2. Finding the discount amount and the selling price
           Marked Price (MP) = Rs. \(5000\)
           Discount Percent (\(D\%\)) = \(5\%\)
          Therefore
           Discount Amount = \(5\%\) of \(5000 =0.05 \times 5000 = 250\)
           So, the discount amount is Rs. \(250\).
      Next
           Selling Price (SP) = MP – Discount = \(5000 - 250 = 4750\)
           So, the selling price is Rs. \(4750\).      
     
3. Finding the cost price
           Selling Price (SP) = Rs. \(4750\)
           Profit Percent (\(P\%\)) = \(10\%\)
           We know that,
           SP = \(110\%\) of CP
           or\(4750 = \dfrac{110}{100} \times CP\)
           or\(CP = \dfrac{4750 \times 100}{110} = 4318.18\) (approx)
           Hence, the cost price of the cycle is approximately Rs. \(4318.18\).      
   
 
13. रञ्जनले एउटा घडी \(25\%\) छुट र \(13\%\) मूल्य अभिवृद्धि करसहित रु. \(3,450\) मा किनिछन् । Ranjan bought a watch for Rs. \(3,450\) with \(25\%\) discount and \(13\%\) value added tax.
    1. मूल्य अभिवृद्धि कर प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find value added tax percent. [1K]
    2. उक्त घडीको VAT बाहेकको मूल्य पत्ता लगाउनुहोस् । Find the price of the watch without VAT. [2U]
    3. उक्त घडीको अङ्कित मूल्य पत्ता लगाउनुहोस् । Find the marked price of the watch. [1U]
 
   
     
1. The formula to find the Value Added Tax percent is:
           VAT Percent = \( \dfrac{\text{VAT Amount}}{\text{Selling Price}} \times 100\% \)
           or\(V\% = \dfrac{\text{VAT}}{\text{SP}} \times 100\% \)      
     
2. Finding the price of the watch without VAT (Selling Price)
           Price with VAT (ASP) = Rs. \(3,450\)
           VAT Percent (\(V\%\)) = \(13\%\)
        We know that,
           ASP = \(113\%\) of SP
           or\(3,450 = \dfrac{113}{100} \times SP\)
           or\(SP = \dfrac{3,450 \times 100}{113} = 3,053.097\) (approx), say Rs 3000
          
     
3. Finding the marked price of the watch
           Selling Price (SP) = Rs. \(3,000\) (assuming a clean number )
           Discount Percent (\(D\%\)) = \(25\%\)
           We know that
           SP = \(75\%\) of MP
           or\(3,000 = 0.75 \times MP\)
           or\(MP = \dfrac{3,000}{0.75} = 4,000\)
           Hence, the marked price of the watch is Rs. \(4,000\).      
   
 
14. एउटा पसलेले पंखाको अङ्कित मूल्य रु. \(3,200\) निर्धारण गरेको रहेछ । उसले \(10\%\) छुट र \(20\%\) नाफामा पंखा बेचे । A shopkeeper fixed the price of a fan to be Rs. \(3,200\). He sold the fan at \(10\%\) discount and still earned a profit of \(20\%\).
    1. छुट भन्नाले के बुझिन्छ ? लेख्नुहोस् । What is meant by discount? Write it. [1K]
    2. उक्त पंखाको विक्रय मूल्य पत्ता लगाउनुहोस् । Find the selling price of the fan. [1U]
    3. कति नाफा कमाएछन् ? पत्ता लगाउनुहोस् । How much profit the shopkeeper made? Find it. [2A]
 
   
     
1. Discount is the reduction in the price of an article from its marked price (MP) to attract customers and increase sales. It is calculated on the marked price.      
     
2. Finding the selling price of the fan
           Marked Price (MP) = Rs. \(3,200\)
           Discount Percent (\(D\%\)) = \(10\%\)
           We know that
           SP = \(90\% \times MP = 0.9 \times 3,200= 2,880\)
           So, the selling price of the fan is Rs. \(2,880\).      
     
3. Finding the profit the shopkeeper made
           Selling Price (SP) = Rs. \(2,880\)
           Profit Percent (\(P\%\)) = \(20\%\)
                   We know that,
           SP = \(120\%\) of CP
           or\(2,880 = 1.2 \times CP\)
                 or\(CP = \dfrac{2,880}{1.2} = 2,400\)
           Now, the Profit Amount is
           Profit = SP – CP = \(2,880 - 2,400 = 480\)
           Hence, the profit the shopkeeper made is Rs. \(480\).      
   
 
15. दयारामले एउटा पुस्तकको अङ्कित मूल्य रु. \(750\) निर्धारण गरेछन् । उनले उक्त पुस्तक रु. \(90\) छुट दिई बेच्दा उनलाई \(50\) नाफा भएछ । Dayaram fixed the marked price of a book to be Rs. \(750\). He sold the book with a discount of Rs. \(90\), still he made a profit of Rs. \(50\).
    1. नाफा प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula of finding profit percent. [1K]
    2. छुट प्रतिशत पत्ता लगाउनुहोस् । Find the discount percent. [1U]
    3. नाफा प्रतिशत कति रहेछ ? पत्ता लगाउनुहोस् । How much is the profit percent? Find it. [2A]
 
   
     
1. The formula to find the profit percent is:
           Profit Percent = \( \dfrac{\text{Profit Amount}}{\text{Cost Price}} \times 100\% \)
           or\(P\% = \dfrac{Profit}{\text{CP}} \times 100\% \)      
     
2. Finding the discount percent
           Marked Price (MP) = Rs. \(750\)
           Discount Amount = Rs. \(90\)
           The formula for Discount Percent is:
           Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
           orDiscount Percent = \( \dfrac{90}{750} \times 100\% = 12\% \)
           So, the discount percent is \(12\%\).      
     
3. Finding the profit percent
                   SP = MP – Discount Amount = \(750 - 90 = 660\)
          Profit Amount = Rs. \(50\)
           CP = SP – Profit Amount = \(660 - 50 = 610\)
      Therefore
   Profit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% = \dfrac{50}{610} \times 100\% =\approx 8.1967\% \)
                
   
 
16. किरणले आफ्नो पसलमा रहेको एउटा क्यामराको अङ्कित मूल्य रु. \(70,000\) निर्धारण गरेछन् । उनले उक्त क्यामरा \(10\%\) छुटमा बेचेछन् । Kiran fixed the marked price of a camera at Rs. \(70,000\) at his shop. He sold it at a \(10\%\) discount on the shop.
    1. क्रय मूल्य र विक्रय मूल्यको बीचको सम्बन्ध कस्तो हुन्छ ? लेख्नुहोस् । What are the relations between cost price and the selling price when there is a profit and there is a loss? [1K]
    2. छुट रकम कति रहेछ ? पत्ता लगाउनुहोस् । How much is the discount amount? Find it. [1U]
    3. \(13\%\) VAT सहितको क्यामराको विक्रय मूल्य पत्ता लगाउनुहोस् । Find the price of the camera with \(13\%\) VAT. [2A]
 
1. The relations between Cost Price (CP)and Selling Price (SP) are:
   SP=CP-Profit
   SP=CP+Loss
     
2. Finding the discount amount
   Marked Price (MP) = Rs. \(70,000\)
   Discount Percent (\(D\%\)) = \(10\%\)
   Discount Amount = \(10\%\) of MP
   orDiscount Amount = \( 0.1 \times 70,000 = 7,000 \)
   So, the discount amount is Rs. \(7,000\).
     
3. Finding the selling price of the camera with \(13\%\) VAT
           SP = MP – Discount = \(70,000 - 7,000 = 63,000\)
   VAT Percent (\(V\%\)) = \(13\%\), so
           ASP = \(113\% \times 63,000\)
           orASP = 1.13 \times 63,000 = 71,190\)
   Hence, the selling price of the camera with \(13\%\) VAT is Rs. \(71,190\).      
   
 
17. बिरेन्द्रले एउटा मोटरसाइकल रु. \(2,00,000\) मा किनेछन् । उनले मोटरसाइकलको अङ्कित मूल्य क्रय मूल्यभन्दा \(25\%\) बढी निर्धारण गरेछन् । उनले उक्त मोटरसाइकल \(10\%\) छुटमा बेचेछन् । Birendra bought a motorcycle for Rs. \(2,00,000\). He fixed the marked price of the motorcycle \(25\%\) above the cost price, then he sold it at \(10\%\) discount.
    1. छुट प्रतिशत र अङ्कित मूल्य दिइएको अवस्थामा विक्रय मूल्य पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find the selling price when discount percent and the marked price are given. [1K]
    2. उक्त मोटरसाइकलको अङ्कित मूल्य पत्ता लगाउनुहोस् । Find the marked price of the motorcycle. [1U]
    3. छुट रकम र विक्रय मूल्य पत्ता लगाउनुहोस् । Find the discount amount and the selling price. [2A]
 
   
     
1. The formula to find the selling price (\(SP\)) when the marked price (\(MP\)) and discount percent (\(D\%\)) are given is:
           \( SP = MP - \dfrac{D}{100} \times MP \)
           or\( SP = (100-D)\% \times MP \)      
     
2. Finding the marked price of the motorcycle
           Cost Price (CP) = Rs. \(2,00,000\)
           Marked Price (MP) is \(25\%\) above CP.
           MP = \(125\%\) of CP
           orMP = 1.25 \times 2,00,000= 2,50,000 \)
           So, the marked price of the motorcycle is Rs. \(2,50,000\).      
     
3. Finding the discount amount and the selling price
           Marked Price (MP) = Rs. \(2,50,000\)
           Discount Percent (\(D\%\)) = \(10\%\)
      Therefore
           Discount=\(10 \% MP= 0.1 \times 2,50,000= 25,000\)
           SP = \(90\% \times MP\) = 0.9 \times 2,50,000= 2,25,000\)
           So, the discount is Rs 25,000 and selling price is Rs. \(2,25,000\).      
   
 
18. एउटा सामानको अङ्कित मूल्य रु. \(25,000\) छ र उक्त सामान रु. \(22,500\) मा बेचिएको छ । The marked price of an article is Rs. \(25,000\) and it is sold for Rs. \(22,500\).
    1. छुट प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find discount percent. [1K]
    2. छुट रकम र छुट प्रतिशत पत्ता लगाउनुहोस् । Find the discount amount and discount percent. [2U]
    3. \(13\%\) VAT सहित उक्त सामानको विक्रय मूल्य कति हुन्छ ? What would be the price of the article with \(13\%\) VAT? [1A]
 
   
     
1. The formula to find the discount percent is:
           Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
           or\(D\% = \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)      
     
2. Finding the discount amount and discount percent
           Marked Price (MP) = Rs. \(25,000\)
           Selling Price (SP) = Rs. \(22,500\)
           So, Discount Amount is
           Discount Amount = MP – SP = \(25,000 - 22,500 = 2,500\)
           Again, Discount Percent is
           Discount Percent = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
           orDiscount Percent = \( \dfrac{2,500}{25,000} \times 100\% = \dfrac{1}{10} \times 100\% = 10\% \)
           So, the discount percent is \(10\%\).      
     
3. Finding the price of the article with \(13\%\) VAT
           Selling Price (SP) = Rs. \(22,500\)
           VAT Percent (\(V\%\)) = \(13\%\)
           The price with VAT (ASP) is
           ASP = \(113\%\) of SP
           orASP =\( 1.13 \times 22,500 = 25,425\)
           Hence, the price of the article with \(13\%\) VAT is Rs. \(25,425\).      
   
 
19. एउटा रेडियो \(10\%\) छुटमा बेच्दा रु. \(1,350\) पर्छ । A radio is sold for Rs. \(1,350\) at \(10\%\) discount.
    1. नोक्सान प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find loss percent. [1K]
    2. उक्त रेडियोको क्रय मूल्य रु. \(1,400\) भए नोक्सान प्रतिशत पत्ता लगाउनुहोस् । If the radio was purchased for Rs. \(1,400\), find the loss percent. [1U]
    3. उक्त रेडियोको अङ्कित मूल्य पत्ता लगाउनुहोस् । Find the marked price of the radio. [2U]
 
   
     
1. The formula to find the loss percent is
           Loss Percent = \( \dfrac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100\% \)
           or\(L\% = \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)      
     
2. Finding the loss percent
           Selling Price (SP) = Rs. \(1,350\)
           Cost Price (CP) = Rs. \(1,400\)
           So, the Loss Amount is
           Loss = CP – SP = \(1,400 - 1,350 = 50\)
           Now, the Loss Percent is
           Loss Percent = \( \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
           orLoss Percent = \( \dfrac{50}{1,400} \times 100\% \approx 3.57\% \)
           So, the loss percent is approximately \(3.57\%\).      
     
3. Finding the marked price of the radio
           Selling Price (SP) = Rs. \(1,350\)
           Discount Percent (\(D\%\)) = \(10\%\)
           Now
           SP = \(90\%\) of MP
           or\(1,350 = 0.9 \times MP\)
               or\(MP = \dfrac{1,350 }{0.9} = 1,500\)
           Hence, the marked price of the radio is Rs. \(1,500\).      
   
 

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