Mathematics: Percentage Type6Priceconsumption Mock Test – Free Online Practice

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Practice Questions (14 of 14)

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1. If the price of a commodity is increased by 25%, by what percentage should its consumption be decreased so that the expenditure of the commodity stays the same?
   यदि किसी वस्तु के मूल्य में 25% की वृद्धि होती है, तो उसके उपभोग में कितने प्रतिशत की कमी की जानी चाहिए ताकि वस्तु पर होने वाला खर्च समान रहे?
   (A) (a) 18.5%

   (B) (b) 20.0%

   (C) (c) 22.5%

   (D) (d) 25.0%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 20.0%

   Explanation: Method 1 (Ratio Method): Price me increase $= 25\% = \frac{1}{4}$. Initial Price : New Price $= 4 : 5$. Hum jante hain ki $\text{Expenditure} = \text{Price} \times \text{Consumption}$. Expenditure constant rakhne ke liye consumption ka ratio price ka ulta hoga: Consumption ratio $= 5 : 4$. Consumption me kami $= 5 - 4 = 1$ unit (5 ke base par). Percentage decrease $= \frac{1}{5} \times 100\% = 20.0\%$. Atah sahi vikalp (b) 20.0% hai. Method 2 (100-Base Method): Initial expenditure $= 100$. Price $25\%$ badhne ke baad cost $= 125$. Kharcha 100 par wapas laane ke liye cut $= 125 - 100 = 25$. 125 ke base par percentage cut: $= \frac{25}{125} \times 100\% = \frac{1}{5} \times 100\% = 20.0\%$. Atah sahi uttar (b) hai.
2. The cost of onions per kg is increased by 200%. A housewife reduces her consumption of onions by 60%. By what percentage does her expenditure on onions increase or decrease?
   प्याज के प्रति किलोग्राम मूल्य में 200% की वृद्धि होती है। एक गृहिणी प्याज के अपने उपभोग में 60% की कमी करती है। प्याज पर उसके खर्च में कितने प्रतिशत की वृद्धि या कमी होती है?
   (A) (a) Decreases, 20%

   (B) (b) Increases, 20%

   (C) (c) Decreases, 25%

   (D) (d) Increases, 25%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) Increases, 20%

   Explanation: Method 1 (Ratio Method): Price: $200\%$ increase ka matlab price $(1 + 2) = 3$ guna ho gaya $\implies$ Price ratio $= 1 : 3$. Consumption: $60\%$ kami $= \frac{3}{5} \implies$ Consumption ratio $= 5 : (5 - 3) = 5 : 2$. $\text{Expenditure} = \text{Price} \times \text{Consumption}$. Initial Expenditure : New Expenditure $= (1 \times 5) : (3 \times 2) = 5 : 6$. Expenditure me increase $= 6 - 5 = 1$ unit (5 ke base par). Percentage increase $= \frac{1}{5} \times 100\% = 20\%$ (Increases, 20%). Atah sahi vikalp (b) Increases, 20% hai. Method 2 (100-Base Method): Initial expenditure $= 100$. Price $200\%$ badhne ke baad intermediate cost $= 100 + 200 = 300$. Consumption $60\%$ ghatne par new expenditure $= 300 - (60\% \text{ of } 300) = 300 - 180 = 120$. Net change over base $100 = 120 - 100 = +20\%$ (Increases, 20%). Atah sahi uttar (b) hai.
3. The cost of wheat is increased by 20% but its consumption is decreased by 25%. Find the percentage increase or decrease in the expenditure of money.
   गेहूं के मूल्य में 20% की वृद्धि होती है लेकिन इसके उपभोग में 25% की कमी आती है। खर्च में होने वाली प्रतिशत वृद्धि या कमी ज्ञात कीजिए।
   (A) (a) 10% decrease

   (B) (b) 10% increase

   (C) (c) 8% decrease

   (D) (d) 5% decrease
   ✅ Answer & Explanation

   Sahi jawab: A) (a) 10% decrease

   Explanation: Method 1 (Ratio Method): Price ($+20\% = \frac{1}{5}$): ratio $= 5 : 6$. Consumption ($-25\% = -\frac{1}{4}$): ratio $= 4 : 3$. $\text{Expenditure} = \text{Price} \times \text{Consumption}$. Initial Expenditure : New Expenditure $= (5 \times 4) : (6 \times 3) = 20 : 18 = 10 : 9$. Expenditure me kami $= 10 - 9 = 1$ unit (10 ke base par). Percentage decrease $= \frac{1}{10} \times 100\% = 10\%$ decrease. Atah sahi vikalp (a) 10% decrease hai. Method 2 (Successive Formula): Net Change $= a + b + \frac{ab}{100}$ Yahan $a = +20\%$ aur $b = -25\%$: $= 20 - 25 + \frac{20 \times (-25)}{100} = -5 - 5 = -10\%$ (10% decrease). Atah sahi uttar (a) hai.
4. When the price of an article increased by 20%, a family reduced its consumption in such a way that the expenditure on it was only 8% more. By what percentage has the family reduced the consumption of the article?
   जब किसी वस्तु के मूल्य में 20% की वृद्धि हुई, तो एक परिवार ने इसके उपभोग में इस प्रकार कमी की कि इस पर होने वाला खर्च केवल 8% ही बढ़ा। परिवार ने वस्तु के उपभोग में कितने प्रतिशत की कमी की?
   (A) (a) 10%

   (B) (b) 12%

   (C) (c) 15%

   (D) (d) 8%
   ✅ Answer & Explanation

   Sahi jawab: A) (a) 10%

   Explanation: Method 1 (Ratio Method): $\text{Expenditure} = \text{Price} \times \text{Consumption} \implies \text{Consumption} = \frac{\text{Expenditure}}{\text{Price}}$. Price ratio ($+20\%$): $100 : 120 = 5 : 6$. Expenditure ratio ($+8\%$): $100 : 108 = 25 : 27$. Consumption ratio $= \frac{25}{5} : \frac{27}{6} = 5 : 4.5 = 10 : 9$. Consumption me kami $= 10 - 9 = 1$ unit (10 ke base par). Percentage reduction $= \frac{1}{10} \times 100\% = 10\%$. Atah sahi vikalp (a) 10% hai. Method 2 (100-Base Method): Initial expenditure $= 100$. Price badhne ke baad cost $= 120$. Target expenditure $= 108$. Consumption me cut required $= 120 - 108 = 12$. 120 ke base par percentage cut: $= \frac{12}{120} \times 100\% = 10\%$. Atah sahi uttar (a) hai.
5. The price of petrol is increased by 25%. A person wants to increase his expenditure by 15% only. By what percentage should he decrease his consumption?
   पेट्रोल के मूल्य में 25% की वृद्धि होती है। एक व्यक्ति अपने खर्च में केवल 15% की वृद्धि करना चाहता है। उसे अपने उपभोग में कितने प्रतिशत की कमी करनी चाहिए?
   (A) (a) 6%

   (B) (b) 8%

   (C) (c) 10%

   (D) (d) 12%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 8%

   Explanation: Method 1 (Ratio Method): Price ratio: $100 : 125 = 4 : 5$. Expenditure ratio: $100 : 115 = 20 : 23$. Consumption ratio $= \frac{\text{Expenditure}}{\text{Price}} = \frac{20}{4} : \frac{23}{5} = 5 : 4.6 = 25 : 23$. Consumption me kami $= 25 - 23 = 2$ units (25 par). Percentage decrease $= \frac{2}{25} \times 100\% = 8\%$. Atah sahi vikalp (b) 8% hai. Method 2 (100-Base Method): Initial Base $= 100$. Price badhkar ho gayi $= 125$. Allowed expenditure $= 115$. Kami kitni karni hogi $= 125 - 115 = 10$. Badhe hue rate 125 ke base par percentage decrease: $= \frac{10}{125} \times 100\% = \frac{2}{25} \times 100\% = 8\%$. Atah sahi uttar (b) hai.
6. The price of sugar is decreased by 20% and therefore a household increased the consumption of sugar by 15 kg to keep the expenditure same. What was the earlier consumption?
   चीनी के मूल्य में 20% की कमी आती है और इसलिए एक परिवार खर्च को समान रखने के लिए चीनी की खपत में 15 किग्रा की वृद्धि कर देता है। पहले की खपत कितनी थी?
   (A) (a) 50 kg

   (B) (b) 60 kg

   (C) (c) 75 kg

   (D) (d) 45 kg
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 60 kg

   Explanation: Method 1 (Ratio Method): Price decrease $= 20\% = \frac{1}{5}$. Price ratio $= 5 : 4$. Expenditure same rakhne ke liye consumption ka ratio price ka ulta hoga: Consumption ratio $= 4 : 5$. Consumption me badhav $= 5 - 4 = 1$ unit. Given: 1 unit $= 15\text{ kg}$. Earlier consumption = 4 units $= 4 \times 15 = 60\text{ kg}$. Atah sahi vikalp (b) 60 kg hai. Method 2 (100-Base Method): Base expenditure $= 100$. Price drop hone ke baad $= 80$. Wapas 100 par aane ke liye consumption badhana hoga $= 100 - 80 = 20$. Percentage increase in consumption $= \frac{20}{80} = \frac{1}{4}$. $\frac{1}{4}$ of original consumption $= 15\text{ kg} \implies \text{Original Consumption} = 15 \times 4 = 60\text{ kg}$. Atah sahi uttar (b) hai.
7. If the price of rice is reduced by 20%, it allows a person to buy 5 kg more rice for ₹1,200. The reduced rate of rice per kg is:
   यदि चावल के मूल्य में 20% की कमी होती है, तो यह एक व्यक्ति को ₹1,200 में 5 किग्रा अधिक चावल खरीदने की अनुमति देता है। चावल का घटा हुआ मूल्य प्रति किग्रा क्या है?
   (A) (a) ₹40

   (B) (b) ₹48

   (C) (c) ₹50

   (D) (d) ₹60
   ✅ Answer & Explanation

   Sahi jawab: B) (b) ₹48

   Explanation: Method 1 (Direct Savings Method): ₹1,200 par total bachat $= 20\% \text{ of } 1200 = \frac{20}{100} \times 1200 = ₹240$. Is ₹240 ki bachat ki wajah se hi 5 kg extra rice milti hai. Reduced Rate per kg $= \frac{₹240}{5\text{ kg}} = ₹48\text{ per kg}$. Atah sahi vikalp (b) ₹48 hai. Method 2 (Ratio Method): Price ratio: $20\% = \frac{1}{5} \implies 5 : 4$. Consumption ratio $= 4 : 5$. Consumption increase $= 5 - 4 = 1$ unit $= 5\text{ kg}$. New total consumption = 5 units $= 5 \times 5 = 25\text{ kg}$. Reduced rate $= \frac{\text{Total Amount}}{\text{New Consumption}} = \frac{1200}{25} = ₹48\text{ per kg}$. Atah sahi uttar (b) hai.
8. A reduction of 20% in the price of detergent powder enables a buyer to obtain 4 kg more for ₹960. The original price of the detergent powder per kg is:
   डिटर्जेंट पाउडर के मूल्य में 20% की कमी एक खरीदार को ₹960 में 4 किग्रा अधिक प्राप्त करने में सक्षम बनाती है। डिटर्जेंट पाउडर का मूल मूल्य प्रति किग्रा क्या है?
   (A) (a) ₹50

   (B) (b) ₹60

   (C) (c) ₹64

   (D) (d) ₹72
   ✅ Answer & Explanation

   Sahi jawab: B) (b) ₹60

   Explanation: Method 1 (Ratio Method): Price ratio: $20\% = \frac{1}{5} \implies 5 : 4$. Consumption ratio $= 4 : 5$. Increase in consumption $= 5 - 4 = 1$ unit. Given: 1 unit $= 4\text{ kg}$. Original consumption = 4 units $= 4 \times 4 = 16\text{ kg}$. Original Price per kg $= \frac{\text{Total Money}}{\text{Original Consumption}} = \frac{960}{16} = ₹60\text{ per kg}$. Atah sahi vikalp (b) ₹60 hai. Method 2 (100-Base / Reduced to Original Method): ₹960 par $20\%$ bachat $= 0.20 \times 960 = ₹192$. Reduced price per kg $= \frac{192}{4} = ₹48\text{ per kg}$. Reduced price original price ka $80\%$ hai: $80\% = 48 \implies 1\% = 0.6 \implies 100\% = ₹60\text{ per kg}$. Atah sahi uttar (b) hai.
9. A reduction of 25% in the price of wheat enables a person to buy 6 kg more for ₹600. What is the original price per kg?
   गेहूं के मूल्य में 25% की कमी एक व्यक्ति को ₹600 में 6 किग्रा अधिक खरीदने में सक्षम बनाती है। गेहूं का मूल मूल्य प्रति किग्रा क्या है?
   (A) (a) ₹25

   (B) (b) ₹30

   (C) (c) ₹33.33

   (D) (d) ₹35
   ✅ Answer & Explanation

   Sahi jawab: C) (c) ₹33.33

   Explanation: Method 1 (Ratio Method): Price ratio: $25\% = \frac{1}{4} \implies 4 : 3$. Consumption ratio $= 3 : 4$. Increase in consumption $= 4 - 3 = 1$ unit. Given: 1 unit $= 6\text{ kg}$. Original consumption = 3 units $= 3 \times 6 = 18\text{ kg}$. Original Price per kg $= \frac{600}{18} = \frac{100}{3} = ₹33.33\text{ per kg}$. Atah sahi vikalp (c) ₹33.33 hai. Method 2 (Direct Savings Method): ₹600 par $25\%$ bachat $= \frac{1}{4} \times 600 = ₹150$. Reduced price per kg $= \frac{150}{6} = ₹25\text{ per kg}$. Original Price $= \frac{\text{Reduced Price}}{1 - 0.25} = \frac{25}{0.75} = \frac{100}{3} = ₹33.33\text{ per kg}$. Atah sahi uttar (c) hai.
10. If the price of a pen decreases by 20%, then a person can buy 4 more pens for ₹160. What is the new price (in ₹) of each pen?
    यदि एक पेन के मूल्य में 20% की कमी होती है, तो एक व्यक्ति ₹160 में 4 पेन अधिक खरीद सकता है। प्रत्येक पेन का नया मूल्य (₹ में) क्या है?
    (A) (a) ₹6

    (B) (b) ₹8

    (C) (c) ₹10

    (D) (d) ₹12
    ✅ Answer & Explanation

    Sahi jawab: B) (b) ₹8

    Explanation: Method 1 (Direct Savings Method): ₹160 par $20\%$ ki bachat $= \frac{20}{100} \times 160 = ₹32$. Is bache hue ₹32 me 4 extra pen aate hain. New Price of each pen $= \frac{₹32}{4} = ₹8$. Atah sahi vikalp (b) ₹8 hai. Method 2 (Ratio Method): Price ratio: $5 : 4$. Quantity ratio: $4 : 5$. Quantity me increase $= 5 - 4 = 1$ unit $= 4\text{ pens}$. New total quantity = 5 units $= 5 \times 4 = 20\text{ pens}$. New Price per pen $= \frac{160}{20} = ₹8$. Atah sahi uttar (b) hai.
11. A 20% decrease in the cost of flour enables a consumer to purchase an additional 4 kg for ₹480. What was the initial price per kg of the flour?
    आटे के मूल्य में 20% की कमी होने से एक उपभोक्ता ₹480 में 4 किग्रा अधिक आटा खरीद सकता है। आटे का प्रारंभिक मूल्य प्रति किग्रा क्या था?
    (A) (a) ₹24

    (B) (b) ₹30

    (C) (c) ₹32

    (D) (d) ₹36
    ✅ Answer & Explanation

    Sahi jawab: B) (b) ₹30

    Explanation: Method 1 (Ratio Method): Price me kami $= 20\% = \frac{1}{5}$. Price ka ratio $= 5 : 4$. Expenditure same rakhne ke liye consumption ka ratio price ka ulta hoga: Consumption ratio $= 4 : 5$. Consumption me badhav $= 5 - 4 = 1$ unit. Given: 1 unit $= 4\text{ kg}$. Initial consumption = 4 units $= 4 \times 4 = 16\text{ kg}$. Initial price per kg $= \frac{\text{Total Money}}{\text{Initial Consumption}} = \frac{480}{16} = ₹30\text{ per kg}$. Atah sahi vikalp (b) ₹30 hai. Method 2 (Direct Savings Method): ₹480 par total savings $= 20\% \text{ of } 480 = \frac{20}{100} \times 480 = ₹96$. Is ₹96 ki wajah se 4 kg extra aata milta hai. Reduced price per kg $= \frac{96}{4} = ₹24\text{ per kg}$. Kyunki reduced price original price ka $80\%$ hai: Original Price $= \frac{24}{0.80} = ₹30\text{ per kg}$. Atah sahi uttar (b) hai.
12. The reduction of 20% in the price of salt enables a person to buy 4 kg more for ₹320. The reduced price of salt per kg (in ₹) is:
    नमक के मूल्य में 20% की कमी होने पर एक व्यक्ति ₹320 में 4 किग्रा अधिक नमक खरीद सकता है। नमक का घटा हुआ मूल्य प्रति किग्रा (₹ में) क्या है?
    (A) (a) ₹16

    (B) (b) ₹18

    (C) (c) ₹20

    (D) (d) ₹22
    ✅ Answer & Explanation

    Sahi jawab: A) (a) ₹16

    Explanation: Method 1 (Direct Savings Method): ₹320 par $20\%$ ki bachat $= \frac{20}{100} \times 320 = ₹64$. Is bachat se 4 kg extra salt milti hai. Reduced price per kg $= \frac{₹64}{4\text{ kg}} = ₹16\text{ per kg}$. Atah sahi vikalp (a) ₹16 hai. Method 2 (Ratio Method): Price ratio: $20\% = \frac{1}{5} \implies 5 : 4$. Consumption ratio $= 4 : 5$. Consumption increase $= 5 - 4 = 1$ unit $= 4\text{ kg}$. New total consumption = 5 units $= 5 \times 4 = 20\text{ kg}$. Reduced rate per kg $= \frac{320}{20} = ₹16\text{ per kg}$. Atah sahi uttar (a) hai.
13. A reduction of 25% in the price of bananas enables a customer to buy 4 more bananas for ₹60. What is the reduced price of bananas per dozen (in ₹)?
    केले के मूल्य में 25% की कमी एक ग्राहक को ₹60 में 4 केले अधिक खरीदने में सक्षम बनाती है। प्रति दर्जन केले का घटा हुआ मूल्य (₹ में) क्या है?
    (A) (a) ₹40

    (B) (b) ₹45

    (C) (c) ₹48

    (D) (d) ₹50
    ✅ Answer & Explanation

    Sahi jawab: B) (b) ₹45

    Explanation: Method 1 (Direct Savings Method): ₹60 par total bachat $= 25\% \text{ of } 60 = \frac{1}{4} \times 60 = ₹15$. Is ₹15 me 4 extra bananas milte hain. Reduced price per banana $= \frac{₹15}{4}$. 1 dozen me 12 bananas hote hain, isliye: Reduced price per dozen $= \frac{15}{4} \times 12 = 15 \times 3 = ₹45$. Atah sahi vikalp (b) ₹45 hai. Method 2 (Ratio Method): Price ratio: $25\% = \frac{1}{4} \implies 4 : 3$. Quantity ratio $= 3 : 4$. Increase in quantity $= 4 - 3 = 1$ unit $= 4\text{ bananas}$. New quantity = 4 units $= 4 \times 4 = 16\text{ bananas}$. Reduced price for 16 bananas $= ₹60$. Reduced price for 1 dozen (12 bananas) $= \frac{60}{16} \times 12 = \frac{15}{4} \times 12 = ₹45$. Atah sahi uttar (b) hai.
14. A reduction of 25% in the price of sugar enables a person to buy 4 kg more for ₹300. What is the original price per kg?
    चीनी के मूल्य में 25% की कमी एक व्यक्ति को ₹300 में 4 किग्रा अधिक चीनी खरीदने में सक्षम बनाती है। चीनी का मूल मूल्य प्रति किग्रा क्या है?
    (A) (a) ₹20.00

    (B) (b) ₹22.50

    (C) (c) ₹25.00

    (D) (d) ₹27.50
    ✅ Answer & Explanation

    Sahi jawab: C) (c) ₹25.00

    Explanation: Method 1 (Ratio Method): Price ratio: $25\% = \frac{1}{4} \implies 4 : 3$. Consumption ratio $= 3 : 4$. Consumption increase $= 4 - 3 = 1$ unit. Given: 1 unit $= 4\text{ kg}$. Original consumption = 3 units $= 3 \times 4 = 12\text{ kg}$. Original price per kg $= \frac{\text{Total Money}}{\text{Original Consumption}} = \frac{300}{12} = ₹25\text{ per kg}$. Atah sahi vikalp (c) ₹25.00 hai. Method 2 (Direct Savings Method): ₹300 par $25\%$ bachat $= \frac{1}{4} \times 300 = ₹75$. Reduced rate per kg $= \frac{75}{4} = ₹18.75\text{ per kg}$. Reduced price original price ka $75\%$ ($0.75$) hai: Original Price $= \frac{18.75}{0.75} = \frac{1875}{75} = ₹25\text{ per kg}$. Atah sahi uttar (c) hai.

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