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A shopkeeper marked an item 25% above its cost price. During a sale, he offered a discount of 10%. What was his profit percentage?
एक दुकानदार ने एक वस्तु पर उसके क्रय मूल्य से 25% अधिक मूल्य अंकित किया। एक सेल के दौरान उसने 10% की छूट की पेशकश की। उसका लाभ प्रतिशत क्या था?
(A) (a) 10%
(B) (b) 12.50%
(C) (c) 15%
(D) (d) 17.5%
✅ Answer & Explanation
Sahi jawab: B) (b) 12.50%Explanation: Method 1 (Ratio Method): Step 1: 25% markup (1/4) ==> CP : MP = 4 : 5 = 40 : 50. Step 2: 10% discount (1/10) ==> MP : SP = 10 : 9 = 50 : 45. Step 3: CP : SP = 40 : 45 = 8 : 9. Step 4: Profit = 9 - 8 = 1 unit. Profit% = (1 / 8) * 100% = 12.5%. Atah sahi vikalp (b) 12.50% hai. Method 2 (100-Base Method): Step 1: Mana CP = 100. MP = 100 + 25 = 125. Step 2: 10% discount on MP ==> SP = 125 - 12.5 = 112.5. Step 3: Profit% = 112.5 - 100 = 12.5%. Atah sahi uttar (b) hai.
A fan's cost price is unknown. A retailer marks it up so that its marked price is ₹5,000. They offer a 20% discount on this marked price. Even after the discount, they make a profit of 25%. What was the original cost price of the fan for the retailer?
एक पंखे का क्रय मूल्य अज्ञात है। एक खुदरा विक्रेता इस पर इस प्रकार मूल्य अंकित करता है कि इसका अंकित मूल्य ₹5,000 हो जाता है। वे इस अंकित मूल्य पर 20% की छूट देते हैं। छूट के बाद भी, वे 25% का लाभ कमाते हैं। खुदरा विक्रेता के लिए पंखे का मूल क्रय मूल्य क्या था?
(A) (a) ₹3,000
(B) (b) ₹3,500
(C) (c) ₹3,200
(D) (d) ₹4,000
✅ Answer & Explanation
Sahi jawab: C) (c) ₹3,200Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - D%) / (100 + P%). CP / MP = (100 - 20) / (100 + 25) = 80 / 125 = 16 / 25. Step 2: MP (25 units) = ₹5,000 ==> 1 unit = 5000 / 25 = 200. Step 3: CP (16 units) = 16 * 200 = ₹3,200. Atah sahi vikalp (c) ₹3,200 hai. Method 2 (100-Base Method): Step 1: SP = MP * (1 - 0.20) = 5000 * 0.80 = ₹4,000. Step 2: Profit = 25% ==> SP = 1.25 * CP = 4000. Step 3: CP = 4000 / 1.25 = ₹3,200. Atah sahi uttar (c) hai.
A shopkeeper allows a discount of 20% on the marked price of an item and thus gains 10%. What is the ratio of the cost price to the marked price of the item?
एक दुकानदार किसी वस्तु के अंकित मूल्य पर 20% की छूट देता है और इस प्रकार 10% का लाभ प्राप्त करता है। वस्तु के क्रय मूल्य का अंकित मूल्य से अनुपात क्या है?
(A) (a) 8 : 11
(B) (b) 7 : 10
(C) (c) 9 : 13
(D) (d) 11 : 14
✅ Answer & Explanation
Sahi jawab: A) (a) 8 : 11Explanation: Method 1 (Ratio Method): Step 1: Sutra: CP / MP = (100 - Discount%) / (100 + Profit%). Step 2: CP / MP = (100 - 20) / (100 + 10) = 80 / 110. Step 3: Saral karne par: CP : MP = 8 : 11. Atah sahi vikalp (a) 8 : 11 hai. Method 2 (100-Base Method): Step 1: Mana SP = ₹88 (LCM of 80 and 110). Step 2: 20% chhoot par MP = 88 / 0.80 = 110. Step 3: 10% labh par CP = 88 / 1.10 = 80. Step 4: CP : MP = 80 : 110 = 8 : 11. Atah sahi uttar (a) hai.
Having initially established the marked price of a particular commodity at a 20% premium over its cost price, a retail vendor subsequently extended an unspecified discount. If, following this concession, the transaction ultimately yielded a profit of 8% on the cost price, what was the exact percentage of the discount given?
प्रारंभ में एक विशेष वस्तु का अंकित मूल्य उसके क्रय मूल्य से 20% अधिक निर्धारित करने के बाद, एक खुदरा विक्रेता ने बाद में एक अनिर्दिष्ट छूट दी। यदि इस छूट के बाद, लेनदेन में अंततः क्रय मूल्य पर 8% का लाभ प्राप्त हुआ, तो दी गई छूट का सटीक प्रतिशत क्या था?
(A) (a) 80%
(B) (b) 50%
(C) (c) 60%
(D) (d) 10%
✅ Answer & Explanation
Sahi jawab: D) (d) 10%Explanation: Method 1 (Ratio Method): Step 1: 20% markup (1/5) ==> CP : MP = 5 : 6 = 100 : 120. Step 2: 8% labh par SP = 108 units. Step 3: Chhoot (Discount) = MP - SP = 120 - 108 = 12 units. Step 4: Discount% = (12 / 120) * 100% = 10%. Atah sahi vikalp (d) 10% hai. Method 2 (100-Base Method): Step 1: Mana CP = 100 ==> MP = 120, SP = 108. Step 2: Discount = 120 - 108 = 12. Step 3: Discount% = (12 / 120) * 100% = 10%. Atah sahi uttar (d) hai.
An article is marked at ₹800. A shop owner allows a discount of 12% and still gains 8%. What is the approximate cost price of the article?
एक वस्तु का अंकित मूल्य ₹800 है। एक दुकान का मालिक 12% की छूट देता है और फिर भी 8% का लाभ कमाता है। वस्तु का अनुमानित क्रय मूल्य क्या है?
(A) (a) ₹640
(B) (b) ₹652
(C) (c) ₹660
(D) (d) ₹680
✅ Answer & Explanation
Sahi jawab: B) (b) ₹652Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - D%) / (100 + P%). CP / MP = (100 - 12) / (100 + 8) = 88 / 108 = 22 / 27. Step 2: MP (27 units) = ₹800 ==> 1 unit = 800 / 27 ≈ 29.63. Step 3: CP (22 units) = 22 * (800 / 27) = 17600 / 27 ≈ ₹651.85 ≈ ₹652. Atah sahi vikalp (b) ₹652 hai. Method 2 (100-Base Method): Step 1: SP = 800 * (1 - 0.12) = 800 * 0.88 = ₹704. Step 2: CP = 704 / 1.08 = 70400 / 108 ≈ ₹651.85 ≈ ₹652. Atah sahi uttar (b) hai.
A shopkeeper gives a 10% discount and still earns 10% profit. The marked price of the item is how many times (correct to 2 decimal places) the cost price?
एक दुकानदार 10% की छूट देता है और फिर भी 10% लाभ कमाता है। वस्तु का अंकित मूल्य क्रय मूल्य का कितना गुना (2 दशमलव स्थानों तक सही) है?
(A) (a) 1.22
(B) (b) 1.24
(C) (c) 1.28
(D) (d) 1.20
✅ Answer & Explanation
Sahi jawab: A) (a) 1.22Explanation: Method 1 (Ratio Method): Step 1: Formula: MP / CP = (100 + Profit%) / (100 - Discount%). MP / CP = (100 + 10) / (100 - 10) = 110 / 90 = 11 / 9. Step 2: Decimal me man nikalne par: 11 / 9 = 1.222... ≈ 1.22 guna. Atah sahi vikalp (a) 1.22 hai. Method 2 (100-Base Method): Step 1: Mana CP = 100 ==> SP = 110. Step 2: 10% discount ke baad SP = 0.90 * MP = 110. Step 3: MP = 110 / 0.90 = 1100 / 9 = 122.22. Step 4: MP / CP = 122.22 / 100 = 1.22. Atah sahi uttar (a) hai.
A dealer sets the marked price of a television 20% higher than its cost price. If he gives a discount of 15% and makes a profit of Rs.300, what is the cost price of the television?
एक डीलर टेलीविजन का अंकित मूल्य उसके क्रय मूल्य से 20% अधिक निर्धारित करता है। यदि वह 15% की छूट देता है और 300 रुपये का लाभ कमाता है, तो टेलीविजन का क्रय मूल्य क्या है?
(A) (a) Rs.10,000
(B) (b) Rs.12,500
(C) (c) Rs.15,000
(D) (d) Rs.18,000
✅ Answer & Explanation
Sahi jawab: C) (c) Rs.15,000Explanation: Method 1 (Ratio Method): Step 1: CP = 100 units ==> MP (20% markup) = 120 units. Step 2: 15% discount on MP (120 units) = 120 * 0.15 = 18 units. Step 3: SP = 120 - 18 = 102 units. Profit = SP - CP = 102 - 100 = 2 units (ya 2% of CP). Step 4: Prashnanusar 2 units = ₹300 ==> 1 unit = 150. Step 5: Cost Price (100 units) = 100 * 150 = ₹15,000. Atah sahi vikalp (c) Rs.15,000 hai. Method 2 (100-Base Method): Step 1: Net Profit% = a + b + (ab / 100) = 20 - 15 - (20 * 15 / 100) = 5 - 3 = 2%. Step 2: 2% of CP = ₹300. Step 3: CP = 300 / 0.02 = ₹15,000. Atah sahi uttar (c) hai.
A shopkeeper marked an item 50% above its cost price. He then offered two successive discounts of 10% and 20% to a customer. If he made a profit of ₹80, at what price did he sell the item to that customer?
एक दुकानदार ने एक वस्तु पर उसके क्रय मूल्य से 50% अधिक मूल्य अंकित किया। उसने फिर एक ग्राहक को 10% और 20% की दो क्रमिक छूट की पेशकश की। यदि उसने ₹80 का लाभ कमाया, तो उसने उस ग्राहक को वह वस्तु किस मूल्य पर बेची?
(A) (a) ₹1,000
(B) (b) ₹1,080
(C) (c) ₹1,120
(D) (d) ₹1,200
✅ Answer & Explanation
Sahi jawab: B) (b) ₹1,080Explanation: Method 1 (Ratio Method): Step 1: Mana CP = 100 units ==> MP = 150 units. Step 2: Kramik chhoot (10% aur 20%) ka net multiplier: SP = 150 * (9 / 10) * (4 / 5) = 150 * (36 / 50) = 3 * 36 = 108 units. Step 3: Profit = SP - CP = 108 - 100 = 8 units. Step 4: Prashnanusar 8 units = ₹80 ==> 1 unit = ₹10. Step 5: Customer ko becha gaya mulya (SP = 108 units) = 108 * 10 = ₹1,080. Atah sahi vikalp (b) ₹1,080 hai. Method 2 (100-Base Method): Step 1: Net discount of 10% and 20% = 10 + 20 - 2 = 28%. Step 2: SP = 1.50 CP * (1 - 0.28) = 1.50 * 0.72 * CP = 1.08 CP. Step 3: Profit = 0.08 CP = ₹80 ==> CP = ₹1,000. Step 4: Selling Price = CP + Profit = 1000 + 80 = ₹1,080. Atah sahi uttar (b) hai.
A retailer marks his goods at 40% above the cost price and allows a 15% discount. What is his profit percentage?
एक खुदरा विक्रेता अपने माल पर क्रय मूल्य से 40% अधिक मूल्य अंकित करता है और 15% की छूट देता है। उसका लाभ प्रतिशत क्या है?
(A) (a) 20%
(B) (b) 19%
(C) (c) 25%
(D) (d) 22%
✅ Answer & Explanation
Sahi jawab: B) (b) 19%Explanation: Method 1 (Ratio Method): Step 1: 40% markup (2/5) ==> CP : MP = 5 : 7 = 100 : 140. Step 2: 15% discount (3/20) ==> MP : SP = 20 : 17. Step 3: Combined ratio CP : SP: CP : SP = (5 * 20) : (7 * 17) = 100 : 119. Step 4: Profit = 119 - 100 = 19 units. Profit% = 19%. Atah sahi vikalp (b) 19% hai. Method 2 (100-Base Method): Step 1: Mana CP = 100 ==> MP = 140. Step 2: 15% discount on MP = 140 * 0.15 = 21. Step 3: SP = 140 - 21 = 119. Step 4: Profit% = 119 - 100 = 19%. Atah sahi uttar (b) hai.
A 35% profit made when a discount of 35% is given on the marked price of an item. When the discount is 45%, then the profit percentage will be:
किसी वस्तु के अंकित मूल्य पर 35% की छूट देने पर 35% का लाभ होता है। जब छूट 45% हो, तो लाभ प्रतिशत क्या होगा:
(A) (a) 17\frac{1}{13}%
(B) (b) 11\frac{3}{13}%
(C) (c) 14\frac{3}{13}%
(D) (d) 13\frac{3}{17}%
✅ Answer & Explanation
Sahi jawab: C) (c) 14\frac{3}{13}%Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - D1%) / (100 + P1%) = (100 - 35) / (100 + 35) = 65 / 135 = 13 / 27. Step 2: Jab discount 45% ho, toh naya SP2: SP2 = MP * (100 - 45)% = 27 * 0.55 = 14.85 units. Step 3: Naya labh = SP2 - CP = 14.85 - 13 = 1.85 units. Step 4: Profit% = (1.85 / 13) * 100% = 185 / 13% = 14\frac{3}{13}%. Atah sahi vikalp (c) 14 3/13% hai. Method 2 (100-Base Method): Step 1: SP1 = 65% of MP = 135% of CP ==> MP = (135 / 65) * CP = (27 / 13) * CP. Step 2: SP2 = 55% of MP = 0.55 * (27 / 13) * CP = (14.85 / 13) * CP. Step 3: Profit% = [(14.85 - 13) / 13] * 100% = (1.85 / 13) * 100% = 14\frac{3}{13}%. Atah sahi uttar (c) hai.
Anu allows a 20% discount on the marked price of an article and still makes a profit of 25%. If she gains ₹44.80 on the sale of the article, then the cost price of the article is:
अनु एक वस्तु के अंकित मूल्य पर 20% की छूट देती है और फिर भी 25% का लाभ कमाती है। यदि उसे वस्तु की बिक्री पर ₹44.80 का लाभ होता है, तो वस्तु का क्रय मूल्य क्या है:
(A) (a) ₹188.80
(B) (b) ₹192.80
(C) (c) ₹184.20
(D) (d) ₹179.20
✅ Answer & Explanation
Sahi jawab: D) (d) ₹179.20Explanation: Method 1 (Ratio Method): Step 1: Labh pratishat = 25% = 1/4 ==> CP : Profit = 4 : 1. Step 2: Prashnanusar 1 unit labh = ₹44.80. Step 3: Cost Price (CP) = 4 units = 4 * 44.80 = ₹179.20. (Note: Yahan CP nikalne ke liye 20% discount ki zaroorat nahi padti kyunki direct profit amount aur profit% diye gaye hain). Atah sahi vikalp (d) ₹179.20 hai. Method 2 (100-Base Method): Step 1: Profit = 25% of CP = ₹44.80. Step 2: CP = 44.80 / 0.25 = 44.80 * 4 = ₹179.20. Atah sahi uttar (d) hai.
A shopkeeper allows a discount of 22% to his customers and still gains 36%. Find the marked price (in ₹) of an article which costs ₹1,092 to the shopkeeper.
एक दुकानदार अपने ग्राहकों को 22% की छूट देता है और फिर भी 36% का लाभ प्राप्त करता है। उस वस्तु का अंकित मूल्य (₹ में) ज्ञात कीजिए जिसकी लागत दुकानदार के लिए ₹1,092 है।
(A) (a) ₹1,792
(B) (b) ₹2,024
(C) (c) ₹1,872
(D) (d) ₹1,904
✅ Answer & Explanation
Sahi jawab: D) (d) ₹1,904Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - D%) / (100 + P%). CP / MP = (100 - 22) / (100 + 36) = 78 / 136 = 39 / 68. Step 2: Prashnanusar CP (39 units) = ₹1,092. 1 unit = 1092 / 39 = 28. Step 3: Marked Price (MP) = 68 units = 68 * 28 = ₹1,904. Atah sahi vikalp (d) ₹1,904 hai. Method 2 (100-Base Method): Step 1: SP = 1092 * (1 + 0.36) = 1092 * 1.36 = ₹1,485.12. Step 2: SP = MP * (1 - 0.22) = 0.78 * MP. Step 3: MP = 1485.12 / 0.78 = ₹1,904. Atah sahi uttar (d) hai.
Ramesh sells an article for Rs 34,440, after allowing an 18% discount on the marked price and still manages to gain 40% profit. If Ramesh sold the article at a 12% discount on the marked price, then what will be his profit, correct to two places of decimals?
रमेश अंकित मूल्य पर 18% की छूट देने के बाद एक वस्तु को ₹34,440 में बेचता है और फिर भी 40% लाभ प्राप्त करने में सफल रहता है। यदि रमेश वस्तु को अंकित मूल्य पर 12% की छूट पर बेचता है, तो उसका लाभ प्रतिशत क्या होगा (दो दशमलव स्थानों तक सही)?
(A) (a) 50.42%
(B) (b) 48.24%
(C) (c) 50.24%
(D) (d) 48.42%
✅ Answer & Explanation
Sahi jawab: C) (c) 50.24%Explanation: Method 1 (Ratio Method): Step 1: CP aur MP ka anupat nikalein: CP / MP = (100 - 18) / (100 + 40) = 82 / 140 = 41 / 70. Step 2: 12% discount par Naya SP2: SP2 = MP * (100 - 12)% = 70 * 0.88 = 61.6 units. Step 3: Naya labh = SP2 - CP = 61.6 - 41 = 20.6 units. Step 4: Profit% = (20.6 / 41) * 100% = 2060 / 41% ≈ 50.2439% ≈ 50.24%. Atah sahi vikalp (c) 50.24% hai. Method 2 (100-Base Method): Step 1: 82% of MP = 140% of CP ==> MP = (140 / 82) * CP. Step 2: At 12% discount, SP = 0.88 * MP = 0.88 * (140 / 82) * CP = (123.2 / 82) * CP = 1.5024 * CP. Step 3: Profit% = 1.5024 - 1 = 50.24%. Atah sahi uttar (c) hai.
A shopkeeper sells an item at 20% discount on the marked price and earns a profit of 90%. If he sells the same item at 40% discount, then his new profit percentage will be:
एक दुकानदार अंकित मूल्य पर 20% की छूट पर एक वस्तु बेचता है और 90% का लाभ अर्जित करता है। यदि वह उसी वस्तु को 40% छूट पर बेचता है, तो उसका नया लाभ प्रतिशत होगा:
(A) (a) 48.2%
(B) (b) 45.8%
(C) (c) 41.8%
(D) (d) 42.5%
✅ Answer & Explanation
Sahi jawab: D) (d) 42.5%Explanation: Method 1 (Ratio Method): Step 1: CP / MP = (100 - 20) / (100 + 90) = 80 / 190 = 8 / 19. Step 2: 40% discount par naya SP2: SP2 = MP * (100 - 40)% = 19 * 0.60 = 11.4 units. Step 3: Naya Labh = SP2 - CP = 11.4 - 8 = 3.4 units. Step 4: Naya Profit% = (3.4 / 8) * 100% = 340 / 8% = 42.5%. Atah sahi vikalp (d) 42.5% hai. Method 2 (100-Base Method): Step 1: SP1 = 0.80 MP = 1.90 CP ==> MP = (1.90 / 0.80) CP = 2.375 CP. Step 2: SP2 = 0.60 MP = 0.60 * 2.375 CP = 1.425 CP. Step 3: Profit% = (1.425 - 1) * 100% = 42.5%. Atah sahi uttar (d) hai.
By selling an article for Rs 2,160, Prashant allows a 20% discount and earns 28% profit. If the article is sold without any discount, the profit will be:
2,160 रुपये में एक वस्तु बेचकर, प्रशांत 20% की छूट देता है और 28% का लाभ कमाता है। यदि वस्तु बिना किसी छूट के बेची जाती है, तो लाभ होगा:
(A) (a) 55%
(B) (b) 60%
(C) (c) 65%
(D) (d) 50%
✅ Answer & Explanation
Sahi jawab: B) (b) 60%Explanation: Method 1 (Ratio Method): Step 1: CP aur MP ka anupat nikalein: CP / MP = (100 - 20) / (100 + 28) = 80 / 128 = 5 / 8. Step 2: Bina kisi chhoot ke bechne par SP = MP = 8 units. Step 3: Labh = MP - CP = 8 - 5 = 3 units. Step 4: Profit% = (3 / 5) * 100% = 60%. Atah sahi vikalp (b) 60% hai. Method 2 (100-Base Method): Step 1: SP = 0.80 MP = 1.28 CP ==> MP = (1.28 / 0.80) CP = 1.60 CP. Step 2: Bina discount ke bikri mulya SP = MP = 1.60 CP. Step 3: Profit% = (1.60 - 1) * 100% = 60%. Atah sahi uttar (b) hai.
The cost price of a fan is Rs 4,400. A merchant wants to make a 24% profit by selling it. At the time of sale, merchant declares a discount of 12% on the marked price. Find the marked price.
एक पंखे का क्रय मूल्य 4,400 रुपये है। एक व्यापारी इसे बेचकर 24% का लाभ कमाना चाहता है। बिक्री के समय, व्यापारी अंकित मूल्य पर 12% की छूट की घोषणा करता है। अंकित मूल्य ज्ञात कीजिए।
(A) (a) ₹2,600
(B) (b) ₹2,060
(C) (c) ₹6,200
(D) (d) ₹6,020
✅ Answer & Explanation
Sahi jawab: C) (c) ₹6,200Explanation: Method 1 (Ratio Method): Step 1: CP aur MP ka anupat sutra se: CP / MP = (100 - 12) / (100 + 24) = 88 / 124 = 22 / 31. Step 2: Prashnanusar CP (22 units) = ₹4,400. 1 unit = 4400 / 22 = 200. Step 3: Marked Price (MP) = 31 units = 31 * 200 = ₹6,200. Atah sahi vikalp (c) ₹6,200 hai. Method 2 (100-Base Method): Step 1: SP = 4400 * 1.24 = ₹5,456. Step 2: SP = MP * (1 - 0.12) = 0.88 * MP. Step 3: MP = 5456 / 0.88 = ₹6,200. Atah sahi uttar (c) hai.
A seller marks up his product by 50% and offers two consecutive discounts of 10% each. What is his profit percentage?
एक विक्रेता अपने उत्पाद पर 50% अधिक मूल्य अंकित करता है और प्रत्येक 10% की दो क्रमिक छूट प्रदान करता है। उसका लाभ प्रतिशत क्या है?
(A) (a) 20.5%
(B) (b) 21.5%
(C) (c) 22.5%
(D) (d) 23.5%
✅ Answer & Explanation
Sahi jawab: B) (b) 21.5%Explanation: Method 1 (Ratio Method): Step 1: 50% markup (+1/2) ==> CP : MP = 2 : 3 = 100 : 150. Step 2: 10% aur 10% ki do kramik chhooton ka fractional multiplier: SP = 150 * (9 / 10) * (9 / 10) = 150 * (81 / 100) = 121.5 units. Step 3: Profit = SP - CP = 121.5 - 100 = 21.5 units. Step 4: Profit% = (21.5 / 100) * 100% = 21.5%. Atah sahi vikalp (b) 21.5% hai. Method 2 (100-Base Method): Step 1: Let CP = 100 ==> MP = 150. Step 2: Net successive discount of 10% and 10% = 10 + 10 - 1 = 19%. Step 3: SP = 150 * (1 - 0.19) = 150 * 0.81 = 121.5. Step 4: Profit% = 121.5 - 100 = 21.5%. Atah sahi uttar (b) hai.
A trader marked an article 40% above its cost price. He then allowed a discount of 20% on the marked price. If the selling price of the article was ₹560, what was its cost price?
एक व्यापारी ने एक वस्तु पर उसके क्रय मूल्य से 40% अधिक मूल्य अंकित किया। उसने फिर अंकित मूल्य पर 20% की छूट दी। यदि वस्तु का विक्रय मूल्य ₹560 था, तो उसका क्रय मूल्य क्या था?
(A) (a) ₹500
(B) (b) ₹209
(C) (c) ₹306
(D) (d) ₹456
✅ Answer & Explanation
Sahi jawab: A) (a) ₹500Explanation: Method 1 (Ratio Method): Step 1: 40% markup (2/5) ==> CP : MP = 5 : 7. Step 2: 20% discount (1/5) ==> MP : SP = 5 : 4. Step 3: Combined ratio CP : SP: CP : SP = (5 * 5) : (7 * 4) = 25 : 28. Step 4: Prashnanusar SP (28 units) = ₹560. 1 unit = 560 / 28 = 20. Step 5: Cost Price (CP) = 25 units = 25 * 20 = ₹500. Atah sahi vikalp (a) ₹500 hai. Method 2 (100-Base Method): Step 1: MP = 1.40 * CP. Step 2: SP = 1.40 * CP * 0.80 = 1.12 * CP. Step 3: 1.12 * CP = 560 ==> CP = 560 / 1.12 = ₹500. Atah sahi uttar (a) hai.
A wholesaler sells a packet of tea to a retailer at a profit of 20%. The retailer then marks up the price by 50% and offers a discount of 20% to the customer. If the customer pays ₹480, find the cost price of the packet for the wholesaler.
एक थोक विक्रेता एक खुदरा विक्रेता को चाय का एक पैकेट 20% के लाभ पर बेचता है। खुदरा विक्रेता फिर कीमत में 50% की वृद्धि करता है और ग्राहक को 20% की छूट देता है। यदि ग्राहक ₹480 का भुगतान करता है, तो थोक विक्रेता के लिए पैकेट का क्रय मूल्य ज्ञात कीजिए।
(A) (a) ₹300.33
(B) (b) ₹320.26
(C) (c) ₹333.33
(D) (d) ₹340.26
✅ Answer & Explanation
Sahi jawab: C) (c) ₹333.33Explanation: Method 1 (Ratio Method): Step 1: Sabhi charano ke fractional multipliers: - Wholesaler labh (20% = +1/5) ==> 6/5 - Retailer markup (50% = +1/2) ==> 3/2 - Customer discount (20% = -1/5) ==> 4/5 Step 2: Wholesaler CP aur Final SP ka composite ratio: Final SP = CP * (6 / 5) * (3 / 2) * (4 / 5) = CP * (36 / 25). Step 3: Prashnanusar 36 units = ₹480. 1 unit = 480 / 36 = 40 / 3. Step 4: Wholesaler CP (25 units) = 25 * (40 / 3) = 1000 / 3 ≈ ₹333.33. Atah sahi vikalp (c) ₹333.33 hai. Method 2 (100-Base Method): Step 1: Combined factor = 1.20 * 1.50 * 0.80 = 1.44. Step 2: 1.44 * CP = 480. Step 3: CP = 480 / 1.44 = 48000 / 144 = 1000 / 3 ≈ ₹333.33. Atah sahi uttar (c) hai.
A retailer buys 50 pens at the marked price of 44 pens. If he sells these pen at a discount of 1% on the marked price, what is profit percentage?
एक खुदरा विक्रेता 44 पेनों के अंकित मूल्य पर 50 पेन खरीदता है। यदि वह इन पेनों को अंकित मूल्य पर 1% की छूट पर बेचता है, तो लाभ प्रतिशत क्या है?
(A) (a) 10%
(B) (b) 12.5%
(C) (c) 12%
(D) (d) 15%
✅ Answer & Explanation
Sahi jawab: B) (b) 12.5%Explanation: Method 1 (Ratio Method): Step 1: Mana 1 pen ka MP = 1 unit. 50 penon ka kul CP = 44 penon ka MP = 44 units. 1 pen ka CP = 44 / 50 = 0.88 unit. Step 2: 1 pen ko 1% chhoot par becha jata hai: 1 pen ka SP = 1 * (1 - 0.01) = 0.99 unit. Step 3: CP aur SP ka anupat: CP : SP = 0.88 : 0.99 = 88 : 99 = 8 : 9. Step 4: Profit = 9 - 8 = 1 unit. Profit% = (1 / 8) * 100% = 12.5%. Atah sahi vikalp (b) 12.5% hai. Method 2 (100-Base Method): Step 1: Mana 1 pen ka MP = ₹100. 50 penon ka CP = 44 * 100 = ₹4,400. Step 2: 50 penon ka SP (1% discount par) = 50 * 99 = ₹4,950. Step 3: Kul Labh = 4950 - 4400 = ₹550. Step 4: Profit% = (550 / 4400) * 100% = (1 / 8) * 100% = 12.5%. Atah sahi uttar (b) hai.
The marked price of a television set is ₹18,000. A shopkeeper gives a discount of 40% and makes a profit of 10%. Find the cost price of the television set.
एक टेलीविजन सेट का अंकित मूल्य ₹18,000 है। एक दुकानदार 40% की छूट देता है और 10% का लाभ कमाता है। टेलीविजन सेट का क्रय मूल्य ज्ञात कीजिए।
(A) (a) ₹7,821\frac{3}{11}
(B) (b) ₹9,531\frac{5}{11}
(C) (c) ₹9,818\frac{2}{11}
(D) (d) ₹8,181\frac{1}{11}
✅ Answer & Explanation
Sahi jawab: C) (c) ₹9,818\frac{2}{11}Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - Discount%) / (100 + Profit%). CP / MP = (100 - 40) / (100 + 10) = 60 / 110 = 6 / 11. Step 2: Prashnanusar MP (11 units) = ₹18,000. 1 unit = 18000 / 11. Step 3: Cost Price (CP) = 6 units = 6 * (18000 / 11) = 108000 / 11. 108000 / 11 ko mishrit bhinn me badlein: 108000 = 11 * 9818 + 2. CP = ₹9,818\frac{2}{11}. Atah sahi vikalp (c) ₹9,818 2/11 hai. Method 2 (100-Base Method): Step 1: SP = 18,000 * (1 - 0.40) = 18,000 * 0.60 = ₹10,800. Step 2: CP = SP / (1 + 0.10) = 10,800 / 1.10 = 108,000 / 11 = ₹9,818\frac{2}{11}. Atah sahi uttar (c) hai.
A shopkeeper gives 20% commission on the retail price of one article and earns 5% profit. If his commission is reduced by 10%, then what is his approximate profit percentage? (Nearest integral value)
एक दुकानदार एक वस्तु के खुदरा मूल्य पर 20% कमीशन देता है और 5% लाभ कमाता है। यदि उसका कमीशन 10% कम कर दिया जाता है, तो उसका अनुमानित लाभ प्रतिशत क्या है? (निकटतम पूर्णांक मान)
(A) (a) 18%
(B) (b) 10%
(C) (c) 15%
(D) (d) 8%
✅ Answer & Explanation
Sahi jawab: A) (a) 18%Explanation: Method 1 (Ratio Method): Step 1: Commission retail price (MP) par di jati hai: 80% of MP = 105% of CP ==> CP / MP = 80 / 105 = 16 / 21. Step 2: Commission dar 10 percentage points kam hokar 10% ho jati hai: Naya SP = MP * (100 - 10)% = 0.90 * 21 = 18.9 units. Step 3: CP = 16 units par naya labh: Profit = 18.9 - 16 = 2.9 units. Step 4: Naya Profit% = (2.9 / 16) * 100% = 290 / 16% = 18.125% ≈ 18%. Atah sahi vikalp (a) 18% hai. Method 2 (100-Base Method): Step 1: Mana Retail Price = 100 ==> SP1 = 80. Step 2: CP = 80 / 1.05 = 1600 / 21 ≈ 76.19. Step 3: Naya SP (10% commission par) = 90. Step 4: Naya Labh = 90 - 76.19 = 13.81. Step 5: Profit% = (13.81 / 76.19) * 100% ≈ 18.12% ≈ 18%. Atah sahi uttar (a) hai.
A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price to the printed price is:
एक दुकानदार मुद्रित मूल्य पर 10% की छूट पर एक पुस्तक बेचकर 12% का लाभ कमाता है। लागत मूल्य का मुद्रित मूल्य से अनुपात क्या है:
(A) (a) 38 : 55
(B) (b) 45 : 56
(C) (c) 55 : 38
(D) (d) 56 : 45
✅ Answer & Explanation
Sahi jawab: B) (b) 45 : 56Explanation: Method 1 (Ratio Method): Step 1: Sutra: CP : MP = (100 - Discount%) : (100 + Profit%). Step 2: Maan rakhne par: CP : MP = (100 - 10) : (100 + 12) = 90 : 112. Step 3: 2 se saral karne par: 90/2 : 112/2 = 45 : 56. Atah sahi vikalp (b) 45 : 56 hai. Method 2 (100-Base Method): Step 1: Mana CP = 100 ==> SP = 112. Step 2: SP = 90% of MP ==> 0.90 * MP = 112 ==> MP = 112 / 0.90 = 1120 / 9. Step 3: CP : MP = 100 : (1120 / 9) = 900 : 1120 = 45 : 56. Atah sahi uttar (b) hai.
A shopkeeper marks an article x% above the cost price and sells it by allowing 30% discount on the marked price. If there is a loss of 4.8%, then what is the value of x?
एक दुकानदार एक वस्तु पर क्रय मूल्य से x% अधिक अंकित करता है और अंकित मूल्य पर 30% की छूट देकर बेचता है। यदि 4.8% की हानि होती है, तो x का मान क्या है?
(A) (a) 36%
(B) (b) 30%
(C) (c) 40%
(D) (d) 60%
✅ Answer & Explanation
Sahi jawab: A) (a) 36%Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - Discount%) / (100 - Loss%). CP / MP = (100 - 30) / (100 - 4.8) = 70 / 95.2 = 700 / 952 = 25 / 34. Step 2: Markup = MP - CP = 34 - 25 = 9 units. Step 3: Markup% (x%) = (9 / 25) * 100% = 36%. Atah x ka man 36% hai. Atah sahi vikalp (a) 36% hai. Method 2 (100-Base Method): Step 1: Mana CP = 100. 4.8% hani par SP = 100 - 4.8 = 95.2. Step 2: SP = MP par 30% chhoot ke baad ==> 0.70 * MP = 95.2. Step 3: MP = 95.2 / 0.70 = 136. Step 4: Markup x% = 136 - 100 = 36%. Atah sahi uttar (a) hai.
An item is marked at ₹150. A customer gets a 10% discount on it. If the seller still makes a profit of 25%, what is the cost price of the item?
एक वस्तु पर ₹150 अंकित है। एक ग्राहक को इस पर 10% की छूट मिलती है। यदि विक्रेता फिर भी 25% का लाभ कमाता है, तो वस्तु का क्रय मूल्य क्या है?
(A) (a) ₹108
(B) (b) ₹120
(C) (c) ₹112
(D) (d) ₹105
✅ Answer & Explanation
Sahi jawab: A) (a) ₹108Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - Discount%) / (100 + Profit%). CP / MP = (100 - 10) / (100 + 25) = 90 / 125 = 18 / 25. Step 2: Prashnanusar MP (25 units) = ₹150. 1 unit = 150 / 25 = 6. Step 3: Cost Price (CP) = 18 units = 18 * 6 = ₹108. Atah sahi vikalp (a) ₹108 hai. Method 2 (100-Base Method): Step 1: SP = 150 * (1 - 0.10) = 150 * 0.90 = ₹135. Step 2: CP = SP / (1 + 0.25) = 135 / 1.25 = 135 * (4 / 5) = 27 * 4 = ₹108. Atah sahi uttar (a) hai.
A merchant fixes the sale price of his goods at 42% above the cost price. He sells his goods at a 15% discount marked price. His percentage of profit (rounded off to the nearest integer) is:
एक व्यापारी अपने माल का विक्रय मूल्य लागत मूल्य से 42% अधिक निर्धारित करता है। वह अपने माल को अंकित मूल्य पर 15% की छूट पर बेचता है। उसका लाभ प्रतिशत (निकटतम पूर्णांक तक) क्या है:
(A) (a) 21%
(B) (b) 35%
(C) (c) 27%
(D) (d) 42%
✅ Answer & Explanation
Sahi jawab: A) (a) 21%Explanation: Method 1 (Ratio Method): Step 1: CP aur MP ka anupat: 42% markup ==> CP : MP = 100 : 142 = 50 : 71. Step 2: 15% discount (3/20) ==> MP : SP = 20 : 17. Step 3: Combined ratio CP : SP: CP : SP = (50 * 20) : (71 * 17) = 1000 : 1207. Step 4: Profit = 1207 - 1000 = 207 units. Step 5: Profit% = (207 / 1000) * 100% = 20.7% ≈ 21%. Atah sahi vikalp (a) 21% hai. Method 2 (100-Base Method): Step 1: Formula: Net Profit% = a + b + (ab / 100). Step 2: a = +42, b = -15. Net% = 42 - 15 - (42 * 15 / 100) = 27 - 6.30 = 20.7% ≈ 21%. Atah sahi uttar (a) hai.
The cost price and the marked price of an item are ₹720 and ₹900 respectively. When it is sold at a discount of x%, then profit is 5x/3%. What is the value of x?
एक वस्तु का क्रय मूल्य और अंकित मूल्य क्रमशः ₹720 और ₹900 है। जब इसे x% की छूट पर बेचा जाता है, तो लाभ 5x/3% होता है। x का मान क्या है?
(A) (a) 7\frac{4}{7}
(B) (b) 8\frac{4}{7}
(C) (c) 5\frac{5}{7}
(D) (d) 5\frac{4}{7}
✅ Answer & Explanation
Sahi jawab: D) (d) 5\frac{4}{7}Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - Discount%) / (100 + Profit%). Step 2: 720 / 900 = (100 - x) / (100 + 5x/3). 4 / 5 = (100 - x) / (100 + 5x/3). Step 3: Vajra-gunankhand (Cross-multiplication) karein: 4 * (100 + 5x/3) = 5 * (100 - x) 400 + 20x/3 = 500 - 5x 20x/3 + 5x = 500 - 400 35x / 3 = 100 Step 4: x = (100 * 3) / 35 = 300 / 35 = 60 / 7 = 8\frac{4}{7}? Wait, let's verify: Wait, 60 / 7 = 8 4/7 (which matches Option b). Let's check option (b): 8 4/7. Atah x = 8\frac{4}{7}. Atah sahi vikalp (b) 8 4/7 hai. Method 2 (100-Base Method): Step 1: SP = 900 * (1 - x/100) = 900 - 9x. Step 2: Profit = SP - CP = (900 - 9x) - 720 = 180 - 9x. Step 3: Profit% = [(180 - 9x) / 720] * 100 = (180 - 9x) / 7.2. Prashnanusar: (180 - 9x) / 7.2 = 5x / 3. 3(180 - 9x) = 36x ==> 540 - 27x = 36x ==> 63x = 540 ==> x = 540 / 63 = 60 / 7 = 8\frac{4}{7}. Atah sahi uttar (b) hai.
A shopkeeper marks an article at a price such that after giving a discount of x%, he gains 20%. If the cost price and the marked price of the article are ₹920 and ₹1472 respectively, then what is the value of x?
एक दुकानदार एक वस्तु पर इस प्रकार मूल्य अंकित करता है कि x% की छूट देने के बाद उसे 20% का लाभ होता है। यदि वस्तु का क्रय मूल्य और अंकित मूल्य क्रमशः ₹920 और ₹1472 हैं, तो x का मान क्या है?
(A) (a) 18
(B) (b) 20
(C) (c) 25
(D) (d) 30
✅ Answer & Explanation
Sahi jawab: C) (c) 25Explanation: Method 1 (Ratio Method): Step 1: Formula: CP / MP = (100 - x) / (100 + 20). Step 2: CP : MP anupat banayein: 920 / 1472. 184 se kaatne par: 920 / 184 = 5, aur 1472 / 184 = 8 ==> CP : MP = 5 : 8. Step 3: 5 / 8 = (100 - x) / 120. 100 - x = (5 * 120) / 8 = 5 * 15 = 75. Step 4: x = 100 - 75 = 25. Atah sahi vikalp (c) 25 hai. Method 2 (100-Base Method): Step 1: SP = CP * 1.20 = 920 * 1.20 = ₹1,104. Step 2: Chhoot = MP - SP = 1472 - 1104 = ₹368. Step 3: Discount% (x) = (368 / 1472) * 100% = (1 / 4) * 100% = 25%. Atah sahi uttar (c) hai.
A wholesaler marks up a batch of 100 identical clocks by 80% on cost and offers a trade discount of 25% to retailers. A retailer purchases all the clocks and spends Rs.48,000. What is the cost price per clock for the wholesaler?
एक थोक विक्रेता 100 समान घड़ियों के बैच पर लागत से 80% अधिक मूल्य अंकित करता है और खुदरा विक्रेताओं को 25% की व्यापारिक छूट प्रदान करता है। एक खुदरा विक्रेता सभी घड़ियाँ खरीदता है और ₹48,000 खर्च करता है। थोक विक्रेता के लिए प्रति घड़ी क्रय मूल्य क्या है?
(A) (a) Rs.355.56
(B) (b) Rs.426.56
(C) (c) Rs.385.56
(D) (d) Rs.435.56
✅ Answer & Explanation
Sahi jawab: A) (a) Rs.355.56Explanation: Method 1 (Ratio Method): Step 1: 80% markup (+4/5) ==> CP : MP = 5 : 9. Step 2: 25% discount (-1/4) ==> MP : SP = 4 : 3. Step 3: Combined ratio CP : SP = (5 * 4) : (9 * 3) = 20 : 27. Step 4: Wholesaler ka kul SP = Retailer ka kul kharch = ₹48,000. 27 units = ₹48,000 ==> 1 unit = 48000 / 27 = 16000 / 9. Step 5: Wholesaler ka 100 ghadiyo ka kul CP (20 units) = 20 * (16000 / 9) = 320000 / 9. Pratyek ghadi ka CP = (320000 / 9) / 100 = 3200 / 9 ≈ ₹355.555... ≈ Rs.355.56. Atah sahi vikalp (a) Rs.355.56 hai. Method 2 (100-Base Method): Step 1: Wholesaler SP factor = 1.80 * (1 - 0.25) = 1.80 * 0.75 = 1.35 * CP. Step 2: 1.35 * Total CP = 48,000 ==> Total CP = 48,000 / 1.35 = 4800000 / 135 = 320000 / 9. Step 3: CP per clock = (320000 / 9) / 100 = 3200 / 9 ≈ Rs.355.56. Atah sahi uttar (a) hai.
A jeweller marks a necklace at 30% above its cost price. She gives a cash discount of ₹150 on the marked price. If the necklace is sold for ₹1800 and she earns a profit of 20%, what is the cost price of the necklace?
एक जौहरी एक हार पर उसके क्रय मूल्य से 30% अधिक मूल्य अंकित करती है। वह अंकित मूल्य पर ₹150 की नकद छूट देती है। यदि हार ₹1800 में बेचा जाता है और वह 20% का लाभ कमाती है, तो हार का क्रय मूल्य क्या है?
(A) (a) ₹1500
(B) (b) ₹1200
(C) (c) ₹1450
(D) (d) ₹1600
✅ Answer & Explanation
Sahi jawab: A) (a) ₹1500Explanation: Method 1 (Ratio Method): Step 1: Necklace ka SP = ₹1800 aur labh = 20% (1/5). CP : SP = 5 : 6. Step 2: SP (6 units) = ₹1800 ==> 1 unit = 1800 / 6 = 300. Step 3: Cost Price (CP) = 5 units = 5 * 300 = ₹1,500. Atah sahi vikalp (a) ₹1500 hai. Method 2 (100-Base Method): Step 1: SP = 120% of CP = ₹1,800. Step 2: CP = 1800 / 1.20 = ₹1,500. Atah sahi uttar (a) hai.