Profit and Loss_Question_8

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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]
    12.  
       
           
    1. The formula to find the discount amount is:
              Discount Amount = \( D\% \times \text{Marked Price} \)
              orDiscount Amount = \( \dfrac{D}{100} \times MP \)      
      2.      
    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.      
    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. \(27,120\).      
      4.    
     
  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]
    13.  
       
           
    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.      
    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.      
    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. \(4318.18\).      
      4.    
     
  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]
    14.  
       
           
    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.      
    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.      
    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. \(4,000\).      
      4.    
     
  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]
    15.  
       
           
    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.      
    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.      
    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. \(480\).      
      4.    
     
  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]
    16.  
       
           
    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.      
    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.      
    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 = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% = \dfrac{50}{610} \times 100\% =\approx 8.1967\% \)
                   
      4.    
     
  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]
    17.  
    1. The relations between Cost Price (CP)and Selling Price (SP) are:
      SP=CP-Profit
      SP=CP+Loss
      2.      
    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.      
    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. \(71,190\).      
      4.    
     
  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]
    18.  
       
           
    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.      
    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.      
    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. \(2,25,000\).      
      4.    
     
  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]
    19.  
       
           
    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.      
    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.      
    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. \(25,425\).      
      4.    
     
  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]
    20.  
       
           
    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.      
    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.      
    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. \(1,500\).      
      4.    
     

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