51. A shopkeeper marks his goods at 32% above the cost price. He sells three-fifth of the goods at the marked price, one-fifth at a discount of 20% on the market price, and the remaining at 40% discount on the marked price. What is his profit/loss percentage?

एक दुकानदार लागत मूल्य से 32% ऊपर अपना माल चिह्नित करता है। वह चिह्नित मूल्य पर तीन-पांचवें माल बेचता है, एक-पांचवां बाजार मूल्य पर 20% की छूट पर, और शेष 40% चिह्नित मूल्य पर बेचता है। उसका लाभ/हानि प्रतिशत क्या है?


Option”D” is correct

Let cost price of goods be Rs.100

Marked price of goods = 100 × 132/100 = Rs.132

Selling price when discount is 20% = 132 × 80/100 = Rs.105.6

Selling price when discount is 40% = 132 × 60/100 = Rs.79.2

Total selling price of goods = 3/5 × 132 + 1/5 × 105.6 + 1/5 × 79.2 = Rs.116.16

∴ Profit percentage = (116.16 – 100)/100 × 100 = 16.16%

52. The selling price of one article after allowing a discount of 15% on its cost price, is the same as the selling price of another article after allowing a discount of 25% on its cost price. If the sum of the cost prices of both the articles is Rs. 640, then find the selling price of each article.

दो वस्तुओं का विक्रय मूल्य उनके क्रय मूल्य पर क्रमशः 15% और 25% की छूट देने पर समान है। यदि दोनों वस्तुओं के क्रय मूल्य का योग 640 रुपये है, तो प्रत्येक वस्तु का विक्रय मूल्य ज्ञात कीजिए।


Option”B” is correct

Let the cost price of 1st article and 2nd article be ‘x’ and ‘y’ respectively.

According to question,

(100 – 15)% × x = (100 – 25)% × y

⇒ 85% × x = 75% × y

⇒ x/y = 15/17

Let the value of x and y be 15t and 17t respectively.

According to question,

⇒ 15t + 17t = 640

⇒ 32t = 640

⇒ t = 20

⇒ 15t = 300

⇒ The cost price of 1st article = Rs. 300

⇒ The selling price of the 1st article = 85% of 300

⇒ Rs. 255

∴ The selling price of each article is Rs. 255.

53. A man purchased a car for Rs. 12 lakh and was insured at 80% of the cost. He sold the car at a 15% loss but had not yet delivered it to the buyer when he met with an accident. After the accident, the car damaged a lot and the insurance company paid 90% of the insured amount. The net difference in the two transactions is:

एक व्यक्ति ने 12 लाख रुपये में एक कार खरीदी और मूल्य के 80% पर बीमा कराया। उसने कार को 15% हानि पर बेच दिया, लेकिन उसने दुर्घटना के समय तक खरीदार को कार नहीं भेजी। दुर्घटना के बाद, कार बहुत क्षतिग्रस्त हो गई और बीमा कंपनी ने बीमित राशि का 90% भुगतान किया। दोनों लेन-देन में कुल अंतर है:


Option”A” is correct

A man purchased a car for price = Rs. 12 lakh

Car was insured at  = 80% of the cost of the car

Car was sold at the loss of = 15%

The percentage of the insured amount paid by the insurance company = 90%

Formula:

x% of a number = Actual number × (x/100)

Given:

SP = 12,00,000 × (85/100) = 10,20,000

Amount paid by the insurance company = 12,00,000 × (80/100) × (90/100) = 8,64,000

∴ Required difference = 10,20,000 – 8,64,000 = 1,56,000 or 1.56 lakhs

54. A shopkeeper earns a profit of 8% on selling a commodity by giving two successive discounts of 10% and 20% on the marked price of the article. The marked price of the item is how much percent more than its cost price?

एक दुकानदार किसी वस्तु के अंकित मूल्य पर 10% और 20% की दो क्रमिक छूटें देते हुए वस्तु बेच कर 8% का लाभ आर्जित करता है l वस्तु का अंकित मूल्य, उसके क्रय मूल्य से कितने प्रतिशत अधिक है?


Option”B” is correct

Equivalent Discount of two successive discounts of 10% and 20%,

⇒ 10 + 20 – (10 × 20)/100

⇒ 30 – 2

⇒ 28% 

A shopkeeper earns an 8% profit

Let the Cost price of an item be Rs. 100

Then the selling price will be Rs. 108

After giving a 28% of discount on MP, he sold an item at Rs. 108

⇒ MP = 108 × 100/72

⇒ MP = 150

MP is more than CP by,

⇒ 150 – 100 = 50

⇒ 50/100 × 100 = 50%

∴ MP is more than CP by 50%. 

55. After allowing three successive discounts of 10%, 20% and 5% on the marked price of an article, it is sold for Rs. 2,394. The cost price of the article is Rs. 2,500. If it is sold at the marked price, then the profit will be?

एक वस्तु के अंकित मूल्य पर 10%, 20% और 5% की तीन क्रमागत छूट देने के बाद, इसे 2,394 रुपए में बेचा जाता है। वस्तु का क्रय मूल्य 2,500 रुपए है। यदि इसे अंकित मूल्य पर बेचा जाता है, तो लाभ होगा?


Option”A” is correct

Let be assume the marked price of the article is x

⇒ x × 90/100 × 80/100 × 95/100 = 2394

⇒ x = 2394/(0.9 × 0.8 × 0.95) = 2394/0.684 = 3500

⇒ Now, profit = 3500 – 2500 = 1000

∴ The required result will be 1000.

56. Three articles are bought at Rs. 400 each. One of them is sold at a loss of 10%. If the other two articles are sold so as to gain 20% on the whole transaction, then what is the gain percentage on the two articles?

तीन वस्तुएँ 400 रुपये प्रत्येक पर खरीदी जाती हैं। उनमें से एक 10% की हानि पर बेची जाती है। यदि अन्य दो वस्तुएं इस प्रकार बेची जाती हैं कि पूरे लेनदेन पर 20% लाभ होता है तो दोनों वस्तुओं का लाभ प्रतिशत क्या है?


Option”A” is correct

Selling price of an article with 10% loss = 400 – 400 × 10%

⇒ 400(1 -10%) = 400(1 – 10/100)

⇒ 400(100 – 10)/100 = 4 × 90 

⇒ 360

The total cost price of 3 articles = 3 × 400

⇒ 1200

Overall transaction gain = 20%

⇒ Overall transaction selling price should be (120/100) × 1200 = 1440

Selling price of other two articles should be (1440 – 360)/2 = 540

Gain from other two article individually is 540 – 400 = 140

Gain percentage = (140/400) × 100 = 35%

∴ The required gain percentage on two article is 35%

57. A vendor bought 15 kg of rice at a certain rate per kg. After a week, he sold 6 kg of the rice at 20% profit, 6 kg at neither profit nor loss and 3 kg at 10% loss. In this transaction, what is his profit percentage?

एक विक्रेता ने एक निश्चित दर पर प्रति किग्रा 15 किग्रा चावल खरीदा। एक सप्ताह के बाद, उसने 6 किग्रा को 20% के लाभ की दर पर बेचा और 6 किलोग्राम को न तो लाभ और न ही हानि पर बेचा और 3 किग्रा को 10% कम मूल्य पर बेचा। इस लेनदेन में, उसका लाभ प्रतिशत क्या है?


Option”D” is correct

Let the rate at which he bought 15kg of rice be x %

As per the question,

⇒ 6 × 20% + 6 × 0% + 3 × (-10%) = 15 × x %

⇒ 120% + 0 – 30% = 15x%

⇒ 15x% = 90%

∴ x% = 6%

58. A publisher sells a book to a wholesale dealer at a profit of 30%. The wholesaler sells the book to a retailer at a profit of 25%. The book is then solid to a customer for Rs.312, by earning a profit of 20%. What is the cost price (in Rs.) of the book for the wholesale dealer?

एक प्रकाशक 30% के लाभ पर थोक व्यापारी को एक पुस्तक बेचता है। थोक व्यापारी खुदरा व्यापारी को 25% के लाभ पर पुस्तक बेचता है। 20% का लाभ अर्जित करके, पुस्तक 312 रुपये में ग्राहक के लिए ठोस है। थोक व्यापारी के लिए पुस्तक की लागत मूल्य (रुपये में) क्या है?


Option”C” is correct

Selling Price of book for customer = Rs.312

Cost price of book for seller who sells to customer = 312 × 100/120 = Rs.260

Selling price of a book for wholesale = Rs.260

∴ Cost price of book for seller = 260 × 100/125 = Rs.208

59. If the selling price is tripled and the cost price is doubled, the profit would become 65%. What is the present profit (in %)?

यदि विक्रय मूल्य तीन गुना हो जाता है और लागत मूल्य दोगुना हो जाता है, तो लाभ 65% हो जायेगा। वर्तमान लाभ (% में) क्या है?


Option”D” is correct

Let the initial cost price be Rs. 100 and then the revised price will be Rs. 200

When profit is 65%,

⇒ Selling price = 200 × 1.65 = Rs. 330

Now as given, the selling price is tripled,

⇒ Initial selling price = 330/3 = Rs. 110

∴ Profit percentage = (110 – 100)/100 × 100 = 10%

60. A person bought 5 articles for 3 rupees. Find at what price should he be able to sell 100 articles in order to get a profit of 25%.

एक व्यक्ति 5 वस्तुओं को 3 रुपए में खरीदता है, तो उसे 100 वस्तुओं को कितनी कीमत में बेचना चाहिए जिससे कि उसे 25% का लाभ प्राप्त हो सके?


Option”A” is correct

A person bought 5 articles for 3 rupees,

⇒ Cost of 100 articles = (3/5) × 100 = Rs. 60

To get a profit of 25%, Selling price = 60 × 125/100 = 75

⇒ Selling price of 100 articles = Rs. 75

∴ Selling price of 100 articles = Rs. 75

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