Class 10 Compulsory Mathematics – कर र मुद्रा विनिमय (Tax and Money Exchange)
Chapter Information
Chapter: कर र मुद्रा विनिमय (Tax and Money Exchange)
Subject: Compulsory Mathematics, Class 10 SEE
Writer: D.R. Simkhada
Publisher: Readmore Publishers & Distributors
Description: Complete notes on Tax and Money Exchange covering formulas, examples, and solved problems as per SEE Nepal curriculum.
अभ्यास (Exercises)
१. (क) एउटा सामान रु. ५०० मा किनेर रु. ६०० मा बेचियो। नाफा प्रतिशत पत्ता लगाउनुहोस्। (An article was bought for Rs. 500 and sold for Rs. 600. Find the profit percentage.)
Solution:
Cost Price (CP) = Rs. 500, Selling Price (SP) = Rs. 600
Profit (P) = SP – CP = 600 – 500 = Rs. 100
Profit % = \(\frac{P}{CP} \times 100\% = \frac{100}{500} \times 100\% = 20\%\)
Hence, the profit percentage is 20%.
१. (ख) एउटा रेडियो रु. २००० मा किनेर रु. १८०० मा बेचियो। नोक्सान प्रतिशत पत्ता लगाउनुहोस्। (A radio was bought for Rs. 2000 and sold for Rs. 1800. Find the loss percentage.)
Solution:
CP = Rs. 2000, SP = Rs. 1800
Loss (L) = CP – SP = 2000 – 1800 = Rs. 200
Loss % = \(\frac{L}{CP} \times 100\% = \frac{200}{2000} \times 100\% = 10\%\)
Hence, the loss percentage is 10%.
२. (क) एउटा घडी रु. ८८० मा बेच्दा एक पसलेले १०% नाफा कमायो। घडीको क्रय मूल्य पत्ता लगाउनुहोस्। (By selling a watch for Rs. 880, a shopkeeper made a profit of 10%. Find the cost price of the watch.)
Solution:
SP = Rs. 880, Profit % (P) = 10%
CP = \(\frac{100 \times SP}{100 + P\%} = \frac{100 \times 880}{100 + 10} = \frac{88000}{110} = 800\)
Hence, CP of the watch is Rs. 800.
२. (ख) एउटा मोबाइल सेट रु. १५,००० मा बेच्दा एक व्यक्तिलाई २५% नोक्सान भयो। मोबाइल सेटको क्रय मूल्य पत्ता लगाउनुहोस्। (By selling a mobile set for Rs. 15,000, a man incurred a loss of 25%. Find the cost price of the mobile set.)
Solution:
SP = Rs. 15,000, Loss % (L) = 25%
CP = \(\frac{100 \times SP}{100 – L\%} = \frac{100 \times 15000}{100 – 25} = \frac{1500000}{75} = 20000\)
Hence, the CP of the mobile set is Rs. 20,000.
३. (क) एक पसलेले एउटा टेबल रु. १५०० मा किन्यो। १५% नाफा कमाउन उसले कतिमा बेच्नुपर्छ? (A shopkeeper bought a table for Rs. 1500. At what price should he sell it to make a profit of 15%?)
Solution:
CP = Rs. 1500, Profit % (P) = 15%
SP = \(\frac{(100 + P\%) \times CP}{100} = \frac{(100 + 15) \times 1500}{100} = 115 \times 15 = 1725\)
Hence, he should sell the table for Rs. 1725.
३. (ख) एक व्यक्तिले एउटा साइकल रु. ६००० मा किन्यो। उसले ३०% नोक्सानमा बेच्न चाहन्छ। विक्रय मूल्य कति हुनुपर्छ? (A man bought a cycle for Rs. 6000. He wants to sell it at a loss of 30%. What should be the selling price?)
Solution:
CP = Rs. 6000, Loss % (L) = 30%
SP = \(\frac{(100 – L\%) \times CP}{100} = \frac{(100 – 30) \times 6000}{100} = 70 \times 60 = 4200\)
Hence, the SP should be Rs. 4200.
४. (क) एउटा ज्याकेटको अंकित मूल्य रु. २५०० छ। यदि पसलेले १०% छुट दिन्छ भने, ज्याकेटको विक्रय मूल्य कति हुन्छ? (The marked price of a jacket is Rs. 2500. If the shopkeeper allows a 10% discount, what will be the selling price of the jacket?)
Solution:
MP = Rs. 2500, Discount % (D) = 10%
SP = \(MP(1 – \frac{D\%}{100}) = 2500(1 – \frac{10}{100}) = 2500 \times \frac{90}{100} = 2250\)
Hence, the SP of the jacket is Rs. 2250.
४. (ख) एक पसलेले २०% छुट दिएर एउटा साडी रु. १८०० मा बेच्यो। अंकित मूल्य कति थियो? (A shopkeeper sold a sari for Rs. 1800 after allowing a 20% discount. What was the marked price?)
Solution:
SP = Rs. 1800, Discount % (D) = 20%
SP = \(MP(1 – \frac{D\%}{100}) \implies 1800 = MP(1 – \frac{20}{100}) \implies MP = \frac{1800 \times 100}{80} = 2250\)
Hence, the MP of the sari was Rs. 2250.
५. (क) रु. ८५० पर्ने क्याल्कुलेटरको १३% भ्याटसहितको मूल्य पत्ता लगाउनुहोस्। (Find the price of a calculator costing Rs. 850 with a 13% VAT.)
Solution:
SP = Rs. 850, VAT % = 13%
Price with VAT = \(SP(1 + \frac{\text{VAT}\%}{100}) = 850(1 + \frac{13}{100}) = 850 \times \frac{113}{100} = 960.5\)
Hence, the price with VAT is Rs. 960.5.
५. (ख) १३% भ्याटसहित एउटा सामानको मूल्य रु. २८२५ छ। भ्याट जोड्नु अघिको मूल्य पत्ता लगाउनुहोस्। (The price of an article including 13% VAT is Rs. 2825. Find the price before VAT was added.)
Solution:
Price with VAT = Rs. 2825, VAT % = 13%
Price with VAT = \(SP(1 + \frac{\text{VAT}\%}{100}) \implies 2825 = SP(\frac{113}{100}) \implies SP = \frac{2825 \times 100}{113} = 2500\)
Hence, the price before VAT was Rs. 2500.
६. (क) एउटा झोलाको अंकित मूल्य रु. १८०० छ। यदि पसलेले १०% छुट दिएर १३% भ्याट लगाउँछ भने, झोलाको अन्तिम मूल्य कति हुन्छ? (The marked price of a bag is Rs. 1800. If the shopkeeper allows a 10% discount and adds 13% VAT, what will be the final price of the bag?)
Solution:
MP = Rs. 1800, Discount % = 10%, VAT % = 13%
Final Price = \(MP(1 – \frac{D\%}{100})(1 + \frac{\text{VAT}\%}{100}) = 1800(\frac{90}{100})(\frac{113}{100}) = 1830.6\)
Hence, the final price of the bag is Rs. 1830.6.
६. (ख) १५% छुट दिएर १३% भ्याट जोडेपछि एउटा घडीको मूल्य रु. २४०१.२५ हुन्छ। घडीको अंकित मूल्य पत्ता लगाउनुहोस्। (The price of a watch after allowing a 15% discount and then adding 13% VAT is Rs. 2401.25. Find the marked price of the watch.)
Solution:
Final Price = Rs. 2401.25, Discount % = 15%, VAT % = 13%
Final Price = \(MP(1 – \frac{D\%}{100})(1 + \frac{\text{VAT}\%}{100}) \implies 2401.25 = MP(\frac{85}{100})(\frac{113}{100}) \implies MP = \frac{2401.25 \times 10000}{85 \times 113} = 2500\)
Hence, the MP of the watch is Rs. 2500.
७. (क) अंकित मूल्यमा २०% छुट दिएपछि १०% नाफा भयो। यदि सामानको क्रय मूल्य रु. ३६०० हो भने, अंकित मूल्य पत्ता लगाउनुहोस्। (After allowing a 20% discount on the marked price, a 10% profit was made. If the cost price of the article is Rs. 3600, find the marked price.)
Solution:
Discount % = 20%, Profit % = 10%, CP = Rs. 3600
SP = \(\frac{(100 + 10) \times 3600}{100} = 3960\)
SP = \(MP(1 – \frac{20}{100}) \implies 3960 = MP(\frac{80}{100}) \implies MP = \frac{3960 \times 100}{80} = 4950\)
Hence, the MP is Rs. 4950.
७. (ख) एउटा सामानको अंकित मूल्य रु. ५००० छ। यदि पसलेले १०% छुट दिन्छ भने, उसले १२.५% नाफा कमाउँछ। सामानको क्रय मूल्य पत्ता लगाउनुहोस्। (The marked price of an article is Rs. 5000. If the shopkeeper allows a 10% discount, he makes a profit of 12.5%. Find the cost price of the article.)
Solution:
MP = Rs. 5000, Discount % = 10%, Profit % = 12.5%
SP = \(5000(1 – \frac{10}{100}) = 4500\)
CP = \(\frac{100 \times 4500}{100 + 12.5} = \frac{450000}{112.5} = 4000\)
Hence, the CP of the article is Rs. 4000.
८. (क) एक एजेन्टले सामानको बिक्रीमा ५% कमिसन पाउँछ। यदि उसले रु. १५००० बराबरको सामान बेच्छ भने, उसको कमिसन पत्ता लगाउनुहोस्। (An agent gets a 5% commission on the sales of goods. If he sells goods worth Rs. 15000, find his commission.)
Solution:
Commission % = 5%, Total Sales = Rs. 15000
Commission Amount = \(\frac{5}{100} \times 15000 = 750\)
Hence, his commission is Rs. 750.
८. (ख) एक विक्रेताले प्रति महिना रु. १२००० तलब र कुल बिक्रीमा १०% कमिसन पाउँछ। यदि उसले एक महिनामा रु. ५०००० को सामान बेच्यो भने, त्यो महिनाको उसको कुल तलब पत्ता लगाउनुहोस्। (A salesman gets a salary of Rs. 12000 per month plus a 10% commission on the total sales. If he sold goods worth Rs. 50000 in a month, find his total salary for that month.)
Solution:
Basic Salary = Rs. 12000, Commission % = 10%, Total Sales = Rs. 50000
Commission Amount = \(10\% \text{ of } 50000 = 5000\)
Total Salary = Basic Salary + Commission Amount = 12000 + 5000 = 17000
Hence, his total salary is Rs. 17000.
९. (क) अमेरिकी डलरको विनिमय दर $१ = रु. १२० छ। $५०० को लागि कति रुपैयाँ साट्न सकिन्छ? (The exchange rate for US Dollar is $1 = Rs. 120. How many rupees can be exchanged for $500?)
Solution:
$1 = Rs. 120
$500 = \(120 \times 500 = \text{Rs. } 60,000\)
So, Rs. 60,000 can be exchanged for $500.
९. (ख) विनिमय दर रु. १५० = १ पाउन्ड स्टर्लिंग छ। रु. ७५००० को लागि कति पाउन्ड साट्न सकिन्छ? (The exchange rate is Rs. 150 = 1 Pound Sterling. How many pounds can be exchanged for Rs. 75000?)
Solution:
Rs. 150 = £1 \(\implies\) Rs. 1 = £\(\frac{1}{150}\)
Rs. 75000 = £\(\frac{1}{150} \times 75000 = £500\)
So, £500 can be exchanged for Rs. 75000.
१०. (क) एउटा बैंकले पैसा साट्दा २% कमिसन लिन्छ। यदि एक व्यक्तिले $८०० लाई नेपाली रुपैयाँमा साट्छ भने, उसले कति कमिसन तिर्नुपर्छ? ($१ = रु. १२२) (A bank takes 2% commission for exchanging money. If a man exchanges $800 into Nepali rupees, how much commission does he have to pay? ($1 = Rs. 122))
Solution:
Exchange Amount = $800, Commission % = 2%, Exchange Rate: $1 = Rs. 122
Amount in NPR = \(800 \times 122 = \text{Rs. } 97600\)
Commission Amount = \(2\% \text{ of } 97600 = \frac{2}{100} \times 97600 = 1952\)
Hence, he has to pay Rs. 1952 as commission.
१०. (ख) एक पर्यटकले $१ = रु. १२५ को विनिमय दरमा रु. ८०,००० लाई अमेरिकी डलरमा साट्यो। यदि बैंकले १.५% कमिसन लिन्छ भने, उसले कति डलर प्राप्त गर्यो? (A tourist exchanged Rs. 80,000 into US dollars at the exchange rate of $1 = Rs. 125. If the bank charges a 1.5% commission, how many dollars did he receive?)
Solution:
Amount = Rs. 80,000, Exchange Rate: $1 = Rs. 125, Commission % = 1.5%
Commission Amount = \(1.5\% \text{ of } 80000 = 1200\)
Remaining amount = 80000 – 1200 = Rs. 78800
Dollars received = \(\frac{78800}{125} = \$630.4\)
Hence, he received $630.4.
११. (क) चीनमा एउटा घडीको मूल्य ५०० युआन छ। नेपालमा आयात गर्दा २०% भन्सार शुल्क लाग्छ। यदि विनिमय दर १ युआन = रु. १६.५० हो भने, नेपालमा घडीको मूल्य पत्ता लगाउनुहोस्। (The price of a watch is 500 Yuan in China. When it is imported to Nepal, a 20% customs duty is levied. If the exchange rate is 1 Yuan = Rs. 16.50, find the price of the watch in Nepal.)
Solution:
Price in China = 500 Yuan, Customs Duty % = 20%, Exchange Rate: 1 Yuan = Rs. 16.50
Price in NPR = \(500 \times 16.50 = \text{Rs. } 8250\)
Customs Duty Amount = \(20\% \text{ of } 8250 = 1650\)
Price in Nepal = 8250 + 1650 = Rs. 9900
Hence, the price of the watch in Nepal is Rs. 9900.
११. (ख) संयुक्त राज्य अमेरिकामा एउटा ल्यापटपको मूल्य $७०० छ। नेपालमा आयात गर्दा १५% भन्सार शुल्क र त्यसपछि १३% भ्याट लाग्छ। यदि विनिमय दर $१ = रु. १२० हो भने, नेपालमा ल्यापटपको मूल्य पत्ता लगाउनुहोस्। (The price of a laptop is $700 in the USA. A 15% customs duty and then 13% VAT is levied on it when imported to Nepal. Find the price of the laptop in Nepal if the exchange rate is $1 = Rs. 120.)
Solution:
Price in USA = $700, Customs Duty % = 15%, VAT % = 13%, Exchange Rate: $1 = Rs. 120
Price in NPR = \(700 \times 120 = \text{Rs. } 84000\)
Price after customs duty = \(84000 + (15\% \text{ of } 84000) = 84000 + 12600 = \text{Rs. } 96600\)
Final Price in Nepal = \(96600 + (13\% \text{ of } 96600) = 96600 + 12558 = \text{Rs. } 109158\)
Hence, the price of the laptop is Rs. 109158.
१२. (क) एक व्यक्तिले दुईवटा घर प्रत्येक रु. २०,००,००० मा बेच्यो। एउटामा २५% नाफा र अर्कोमा २५% नोक्सान भयो। सम्पूर्ण कारोबारमा उसको कुल नाफा वा नोक्सान प्रतिशत पत्ता लगाउनुहोस्। (A man sold two houses for Rs. 20,00,000 each. He made a profit of 25% on one and incurred a loss of 25% on the other. Find his total gain or loss percentage in the whole transaction.)
Solution:
1st house: SP = Rs. 20,00,000, Profit % = 25% \(\implies\) CP = \(\frac{100 \times 2000000}{125} = 16,00,000\)
2nd house: SP = Rs. 20,00,000, Loss % = 25% \(\implies\) CP = \(\frac{100 \times 2000000}{75} = 26,66,666.67\)
Total SP = 40,00,000, Total CP = 42,66,666.67
Loss = 2,66,666.67
Loss % = \(\frac{266666.67}{4266666.67} \times 100\% = 6.25\%\)
Shortcut: Loss % = \((\frac{25}{10})^2\% = 6.25\%\)
Hence, his total loss is 6.25%.
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