Mathematics: Percentage Type2Increase Decrease Mock Test – Free Online Practice

Mathematics: Percentage Type2Increase Decrease ke liye free mock test: 10 questions, timer, negative marking aur explanation ke saath. Koi login nahi, koi payment nahi — turant shuru karein.

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Practice Questions (10 of 10)

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1. If the price of a product increases by 60%, by what percent should the consumption be reduced to keep the expenditure same?
   यदि किसी वस्तु के मूल्य में 60% की वृद्धि होती है, तो खर्च को समान रखने के लिए उपभोग में कितने प्रतिशत की कमी की जानी चाहिए?
   (A) (a) 35%

   (B) (b) 37.5%

   (C) (c) 40%

   (D) (d) 42.5%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 37.5%

   Explanation: Method 1 (Ratio / Inverse Relation Method): Price increase $= 60\% = \frac{3}{5}$. Initial Price : Increased Price $= 5 : 8$. Since $\text{Expenditure} = \text{Price} \times \text{Consumption} = \text{Constant}$, Consumption must be inversely proportional to price: Initial Consumption : Reduced Consumption $= 8 : 5$. Reduction in consumption $= 8 - 5 = 3$ units on base of 8 units. Percentage reduction $= \frac{3}{8} \times 100\% = 37.5\%$. Hence, correct option is (b) 37.5%. Method 2 (100-Base Method): Let initial expenditure $= 100$. Price increases by $60\% \implies$ New cost $= 160$. To keep the expenditure at 100, the reduction needed $= 160 - 100 = 60$. This reduction of 60 must be calculated on the increased base of 160: Percentage reduction $= \frac{60}{160} \times 100\% = 37.5\%$. Hence, correct answer is (b).
2. The price of pulses has increased by 35%. By what percentage (rounded off to the nearest integer) the increased price of the pulses should be reduced so that the price of the pulses remains unaltered?
   दालों के मूल्य में 35% की वृद्धि हुई है। दालों के बढ़े हुए मूल्य को कितने प्रतिशत (निकटतम पूर्णांक तक) कम किया जाना चाहिए ताकि दालों का मूल्य अपरिवर्तित रहे?
   (A) (a) 24%

   (B) (b) 26%

   (C) (c) 28%

   (D) (d) 30%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 26%

   Explanation: Method 1 (Ratio Method): Price increase $= 35\% = \frac{7}{20}$. Initial Price : Increased Price $= 20 : (20 + 7) = 20 : 27$. To restore the original price, reduction required $= 27 - 20 = 7$ units. Percentage reduction $= \frac{7}{27} \times 100\% = \frac{700}{27}\% \approx 25.925\% \approx 26\%$. Hence, correct option is (b) 26%. Method 2 (100-Base Method): Let initial price $= 100$. Increased price $= 100 + 35 = 135$. Reduction required to return to $100 = 135 - 100 = 35$. Percentage reduction on $135$: $= \frac{35}{135} \times 100\% = \frac{7}{27} \times 100\% \approx 25.925\% \approx 26\%$. Hence, correct answer is (b).
3. A population falls by 15% in the first year. By what percentage must it increase in the second year so that at the end of the second year the population is exactly the same as the original?
   पहले वर्ष में एक जनसंख्या में 15% की गिरावट आती है। दूसरे वर्ष में इसमें कितने प्रतिशत की वृद्धि होनी चाहिए ताकि दूसरे वर्ष के अंत में जनसंख्या मूल जनसंख्या के बिल्कुल समान हो जाए?
   (A) (a) 15.6%

   (B) (b) 16.8%

   (C) (c) 17.6%

   (D) (d) 18.2%
   ✅ Answer & Explanation

   Sahi jawab: C) (c) 17.6%

   Explanation: Method 1 (Ratio Method): Decline in population $= 15\% = \frac{3}{20}$. Original Population : Decreased Population $= 20 : 17$. To return to 20, increase needed $= 20 - 17 = 3$ units. Percentage increase on base 17 units: $= \frac{3}{17} \times 100\% = \frac{300}{17}\% \approx 17.647\% \approx 17.6\%$. Hence, correct option is (c) 17.6%. Method 2 (100-Base Method): Let initial population $= 100$. After $15\%$ decrease, population $= 85$. Increase required $= 100 - 85 = 15$. Percentage increase on base $85$: $= \frac{15}{85} \times 100\% = \frac{3}{17} \times 100\% \approx 17.6\%$. Hence, correct answer is (c).
4. The salary of employees in a factory was reduced by 25% due to economic crisis. In order to have their salary back to original amount, it must be raised by:
   आर्थिक संकट के कारण एक कारखाने में कर्मचारियों के वेतन में 25% की कमी की गई। उनका वेतन मूल राशि पर वापस लाने के लिए इसमें कितनी वृद्धि की जानी चाहिए?
   (A) (a) 25%

   (B) (b) 30%

   (C) (c) 33\frac{1}{3}%

   (D) (d) 40%
   ✅ Answer & Explanation

   Sahi jawab: C) (c) 33\frac{1}{3}%

   Explanation: Method 1 (Ratio Method): Reduction in salary $= 25\% = \frac{1}{4}$. Original Salary : Reduced Salary $= 4 : 3$. Increase required to restore original salary $= 4 - 3 = 1$ unit. Percentage raise on reduced base 3 units: $= \frac{1}{3} \times 100\% = 33\frac{1}{3}\%$. Hence, correct option is (c) 33 1/3%. Method 2 (100-Base Method): Let original salary $= 100$. Reduced salary $= 100 - 25 = 75$. Amount to be raised $= 100 - 75 = 25$. Percentage raise on $75$: $= \frac{25}{75} \times 100\% = \frac{1}{3} \times 100\% = 33\frac{1}{3}\%$. Hence, correct answer is (c).
5. If Ramu's salary is 40% less than Somu's salary, then by how much percent is Somu's salary more than Ramu's salary?
   यदि रामू का वेतन सोमु के वेतन से 40% कम है, तो सोमु का वेतन रामू के वेतन से कितने प्रतिशत अधिक है?
   (A) (a) 60%

   (B) (b) 66.67%

   (C) (c) 70%

   (D) (d) 75%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 66.67%

   Explanation: Method 1 (Ratio Method): $40\% = \frac{2}{5}$. Somu's salary = 5 units, Ramu's salary $= 5 - 2 = 3$ units. Excess of Somu's salary $= 5 - 3 = 2$ units. Percentage more than Ramu (base = 3 units): $= \frac{2}{3} \times 100\% = 66.67\%$. Hence, correct option is (b) 66.67%. Method 2 (100-Base Method): Let Somu's salary $= 100$, then Ramu's salary $= 60$. Excess $= 100 - 60 = 40$. Percentage comparison on Ramu's base: $= \frac{40}{60} \times 100\% = \frac{2}{3} \times 100\% = 66.67\%$. Hence, correct answer is (b).
6. Shyam's income is 25% less than Ram's. How much is Ram's income more than Shyam's in percentage terms?
   श्याम की आय राम की आय से 25% कम है। प्रतिशत के रूप में राम की आय श्याम की आय से कितनी अधिक है?
   (A) (a) 20%

   (B) (b) 25%

   (C) (c) 33\frac{1}{3}%

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

   Sahi jawab: C) (c) 33\frac{1}{3}%

   Explanation: Method 1 (Ratio Method): $25\% = \frac{1}{4}$. Ram's income = 4 units, Shyam's income $= 4 - 1 = 3$ units. Excess of Ram's income $= 4 - 3 = 1$ unit. Percentage more than Shyam (base = 3 units): $= \frac{1}{3} \times 100\% = 33\frac{1}{3}\%$. Hence, correct option is (c) 33 1/3%. Method 2 (100-Base Method): Let Ram's income $= 100$, then Shyam's income $= 75$. Excess $= 100 - 75 = 25$. Percentage comparison on Shyam's base ($75$): $= \frac{25}{75} \times 100\% = 33\frac{1}{3}\%$. Hence, correct answer is (c).
7. If the price of a product increases by 30%, by what percent should the consumption be reduced to keep the expenditure same?
   यदि किसी वस्तु के मूल्य में 30% की वृद्धि होती है, तो खर्च को समान रखने के लिए उपभोग में कितने प्रतिशत की कमी की जानी चाहिए?
   (A) (a) 21.5%

   (B) (b) 23.08%

   (C) (c) 25.5%

   (D) (d) 27.27%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 23.08%

   Explanation: Method 1 (Ratio / Inverse Relation Method): Price increase $= 30\% = \frac{3}{10}$. Price Ratio $= 10 : 13 \implies$ Consumption Ratio $= 13 : 10$. Reduction in consumption $= 13 - 10 = 3$ units on base of 13 units. Percentage reduction $= \frac{3}{13} \times 100\% = \frac{300}{13}\% \approx 23.08\%$. Hence, correct option is (b) 23.08%. Method 2 (100-Base Method): Let initial expenditure $= 100$. New cost $= 130$. Reduction needed $= 130 - 100 = 30$. Percentage reduction on $130$: $= \frac{30}{130} \times 100\% = \frac{3}{13} \times 100\% \approx 23.08\%$. Hence, correct answer is (b).
8. If the price of tea is increased by 50%, by what percentage must the consumption of tea be decreased so as not to increase the expenditure?
   यदि चाय के मूल्य में 50% की वृद्धि होती है, तो चाय के उपभोग में कितने प्रतिशत की कमी की जानी चाहिए ताकि खर्च में कोई वृद्धि न हो?
   (A) (a) 25%

   (B) (b) 30%

   (C) (c) 33.33%

   (D) (d) 40%
   ✅ Answer & Explanation

   Sahi jawab: C) (c) 33.33%

   Explanation: Method 1 (Ratio Method): Price increase $= 50\% = \frac{1}{2}$. Price Ratio $= 2 : 3 \implies$ Consumption Ratio $= 3 : 2$. Reduction in consumption $= 3 - 2 = 1$ unit on base of 3 units. Percentage decrease $= \frac{1}{3} \times 100\% = 33.33\%$. Hence, correct option is (c) 33.33%. Method 2 (100-Base Method): Initial expenditure $= 100$. Increased cost $= 150$. Reduction needed $= 150 - 100 = 50$. Percentage reduction on $150$: $= \frac{50}{150} \times 100\% = \frac{1}{3} \times 100\% = 33.33\%$. Hence, correct answer is (c).
9. Due to fall in manpower, the production in a factory decreases by 40%. By what percentage should the working hours be increased to restore the original production?
   श्रमशक्ति (manpower) में कमी के कारण, एक कारखाने में उत्पादन 40% कम हो जाता है। मूल उत्पादन को पुनः प्राप्त करने के लिए कार्य के घंटों में कितने प्रतिशत की वृद्धि की जानी चाहिए?
   (A) (a) 60%

   (B) (b) 66.67%

   (C) (c) 75%

   (D) (d) 80%
   ✅ Answer & Explanation

   Sahi jawab: B) (b) 66.67%

   Explanation: Method 1 (Ratio Method): Production decrease $= 40\% = \frac{2}{5}$. Original Production : Reduced Production $= 5 : 3$. Working Hours Ratio $= 3 : 5$. Increase in working hours $= 5 - 3 = 2$ units on base of 3 units. Percentage increase $= \frac{2}{3} \times 100\% = 66.67\%$. Hence, correct option is (b) 66.67%. Method 2 (100-Base Method): Initial production $= 100$. Reduced production $= 60$. Increase needed to reach $100 = 100 - 60 = 40$. Percentage increase on current base $60$: $= \frac{40}{60} \times 100\% = \frac{2}{3} \times 100\% = 66.67\%$. Hence, correct answer is (b).
10. By what percent the new price of an article must be increased to restore its former value, if the cost of the article was reduced by 20% in the past?
    किसी वस्तु के नए मूल्य में कितने प्रतिशत की वृद्धि की जानी चाहिए ताकि उसका पुराना मूल्य पुनः प्राप्त हो सके, यदि अतीत में वस्तु के मूल्य में 20% की कटौती की गई थी?
    (A) (a) 20%

    (B) (b) 22.5%

    (C) (c) 25%

    (D) (d) 30%
    ✅ Answer & Explanation

    Sahi jawab: C) (c) 25%

    Explanation: Method 1 (Ratio Method): Price reduction $= 20\% = \frac{1}{5}$. Original Price : Reduced Price $= 5 : 4$. Increase needed to restore original price $= 5 - 4 = 1$ unit on base of 4 units. Percentage increase $= \frac{1}{4} \times 100\% = 25\%$. Hence, correct option is (c) 25%. Method 2 (100-Base Method): Let former value $= 100$. New price after $20\%$ cut $= 80$. Addition required $= 100 - 80 = 20$. Percentage raise on base $80$: $= \frac{20}{80} \times 100\% = \frac{1}{4} \times 100\% = 25\%$. Hence, correct answer is (c).

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