Competitive Exams : Quantitative Aptitude - Percentage (Set 9) | Concept of Maths

Question 1

1. In a high-end electronics laboratory, the price of a precision oscilloscope was increased by 20%. Due to a technical upgrade, the demand then decreased by x%. If the total revenue of the manufacturer increased by 8%, find the value of x.

A) 12%

B) 8%

C) 10%

D) 15%

Answer

Correct Answer: C

Revenue = Price $\\times$ Quantity. Let initial Price = P and Quantity = Q. Initial Revenue = PQ. New Price = 1.20P. New Quantity = $Q(1 - \\frac{x}{100})$. New Revenue = 1.08PQ. $$1.20P \\times Q(1 - \\frac{x}{100}) = 1.08PQ$ $1.2(1 - \\frac{x}{100}) = 1.08 \\Rightarrow 1 - \\frac{x}{100} = 0.9$ $\\frac{x}{100} = 0.1 \\Rightarrow x = 10$$.

Question 2

2. In a lunar colony, the population of engineers increases by 15% in the first year and decreases by 10% in the second year. In the third year, it increases by 20%. If the population at the end of 3 years is 14,904, what was the initial population?

A) 11,500

B) 12,000

C) 12,500

D) 10,800

Answer

Correct Answer: B

Let initial population be P. Population after 3 years = $P \\times 1.15 \\times 0.90 \\times 1.20 = 14904$. $P \\times (\\frac{115}{100} \\times \\frac{90}{100} \\times \\frac{120}{100}) = 14904$ $P \\times (1.15 \\times 1.08) = 14904$ $P \\times 1.242 = 14904$ $P = \\frac{14904}{1.242} = 12000$.

Question 3

3. An alloy of Titanium and Nickel contains 35% Titanium. If 15 kg of pure Nickel is added to 45 kg of this alloy, what is the new percentage of Titanium in the mixture?

A) 26.25%

B) 28.5%

C) 24.75%

D) 30%

Question 4

4. In an exam, 80% of the candidates passed in Advanced Physics and 75% passed in Applied Mathematics. If 10% failed in both subjects and 260 candidates passed in both, find the total number of candidates who appeared for the exam.

A) 350

B) 420

C) 500

D) 400

Answer

Correct Answer: D

Let total candidates be 100\%. Failed in both = 10\%. Passed in at least one = 100 - 10 = 90\%. Let P be Physics and M be Mathematics. $n(P \\cup M) = n(P) + n(M) - n(P \\cap M)$. $90\% = 80\% + 75\% - n(P \\cap M)$ $n(P \\cap M) = 155\% - 90\% = 65\%$. Given 65\% of Total = 260. Total = $\\frac{260 \\times 100}{65} = 4 \\times 100 = 400$.

Question 5

5. A data center consumes 40% of its power for servers and 35% for cooling. Out of the remaining power, 60% is used for lighting and security. If the power left for other administrative tasks is 300 kW, what is the total power consumption?

A) 2500 kW

B) 3000 kW

C) 2800 kW

D) 3200 kW

Answer

Correct Answer: B

Power for Servers + Cooling = 40\% + 35\% = 75\%. Remaining power = 100\% - 75\% = 25\%. Power for Lighting & Security = 60\% of 25\% = 15\%. Remaining power for Admin = 25\% - 15\% = 10\%. 10\% of Total = 300 kW \\Rightarrow Total = 3000 kW.

Question 6

6. The radius of a cylindrical fuel storage tank is increased by 25% and its height is decreased by 20%. What is the percentage change in the volume of the tank?

A) No change

B) 15% increase

C) 25% increase

D) 10% decrease

Answer

Correct Answer: C

Volume $V = \\pi r^2 h$. New radius r' = 1.25r, New height h' = 0.80h. New Volume $V' = \\pi (1.25r)^2 (0.80h) = \\pi (1.5625 r^2) (0.80 h)$. $V' = 1.5625 \\times 0.80 \\times V = 1.25 V$. Percentage increase = $(1.25 - 1) \\times 100 = 25\%$.

Question 7

7. In a multi-candidate election, Candidate Alpha received 48% of the valid votes. 20% of the total votes were declared invalid. If the total number of votes was 15,000, find the number of valid votes received by other candidates combined.

A) 6,240

B) 5,800

C) 7,200

D) 6,500

Answer

Correct Answer: A

Total votes = 15,000. Invalid = 20\% of 15,000 = 3,000. Valid votes = 15,000 - 3,000 = 12,000. Alpha's votes = 48\% of 12,000 = 5,760. Others' combined valid votes = 12,000 - 5,760 = 6,240.

Question 8

8. A pharmaceutical solution contains 12% of a specific compound. After 8 liters of water evaporates, the concentration of the compound becomes 16%. What was the original volume of the solution?

A) 24 liters

B) 40 liters

C) 36 liters

D) 32 liters

Answer

Correct Answer: D

Let original volume be V. Amount of compound = 0.12V. After evaporation, volume = V - 8. Amount of compound (remains same) = 0.16(V - 8). $0.12V = 0.16V - 1.28 $0.04V = 1.28 \\Rightarrow V = \\frac{1.28}{0.04} = 32 \ liters.$$

Question 9

9. If x% of y is equal to z, then what percentage of z is x?

A) $\frac{100^2}{y}$

B) $\frac{10000}{y}$

C) $\frac{y}{100}$

D) $\frac{y}{10000}$

Answer

Correct Answer: B

Given: $\\frac{x}{100} \\times y = z \\Rightarrow z = \\frac{xy}{100}$. We need to find k such that $\\frac{k}{100} \\times z = x$. $\\frac{k}{100} \\times (\\frac{xy}{100}) = x$ $\\frac{ky}{10000} = 1 \\Rightarrow k = \\frac{10000}{y}$.

Question 10

10. The price of a specialized software license decreases by 10% every year. If the price today is 14,580, what was its price 3 years ago?

A) 18,000

B) 19,500

C) 20,000

D) 21,000

Answer

Correct Answer: C

Let price 3 years ago be P. $P \\times (1 - 0.10)^3 = 14580$ $P \\times (0.9)^3 = 14580$ $P \\times 0.729 = 14580$ $P = \\frac{14580}{0.729} = 20000$.

Question 11

11. A student scored 32% marks in an aptitude test and failed by 12 marks. Another student scored 42% marks and got 28 marks more than the minimum passing marks. What is the passing percentage?

A) 35%

B) 38%

C) 34%

D) 36%

Answer

Correct Answer: A

Let total marks be T. Passing marks $P_{pass}$. $0.32T + 12 = P_{pass}$ $0.42T - 28 = P_{pass}$ 0.42T - 0.32T = 12 + 28 \\Rightarrow 0.10T = 40 \\Rightarrow T = 400. $P_{pass} = 0.32(400) + 12 = 128 + 12 = 140$. Passing Percentage = $(\\frac{140}{400}) \\times 100 = 35\%$.

Question 12

12. If the income tax is increased by 19%, the net income is reduced by 1%. What is the rate of income tax?

A) 4%

B) 6%

C) 5%

D) 7.5%

Answer

Correct Answer: C

Net Income = Gross Income - Tax. Change in Tax = Change in Net Income. 19\% of Tax = 1\% of Net Income. $\\frac{\Tax}{\Net Income} = \\frac{1}{19}$. Gross Income = Tax + Net Income = 1 + 19 = 20. Tax Rate = $(\\frac{\Tax}{\Gross Income}) \\times 100 = \\frac{1}{20} \\times 100 = 5\%$.

Question 13

13. In a stock market cycle, a portfolio value increases by 25% in the first quarter, then decreases by 20% in the second, and finally increases by 10% in the third. What is the net percentage change over the three quarters?

A) 15% increase

B) 5% increase

C) 12% increase

D) 10% increase

Answer

Correct Answer: D

Net Change Multiplier = $1.25 \\times 0.80 \\times 1.10$. $(1.25 \\times 0.80) = 1.00$. $1.00 \\times 1.10 = 1.10$. Net change = $(1.10 - 1) \\times 100 = 10\%$ increase.

Question 14

14. A vessel is filled with a liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A) $\frac{1}{4}$

B) $\frac{1}{5}$

C) $\frac{1}{7}$

D) $\frac{1}{3}$

Answer

Correct Answer: B

Ratio W:S = 3:5. Let total volume be 8 units (3W, 5S). Draw off x units. Remaining syrup = $5 - (\\frac{5}{8})x$. In final mixture (8 units), syrup should be 4 units (half). $5 - \\frac{5}{8}x = 4 \\Rightarrow \\frac{5}{8}x = 1 \\Rightarrow x = \\frac{8}{5}$. Fraction of mixture drawn off = $\\frac{x}{\Total} = \\frac{8/5}{8} = \\frac{1}{5}$.

Question 15

15. The price of sugar is increased by $33\frac{1}{3}%$. By what percentage must a household reduce the consumption of sugar so that the expenditure on sugar remains the same?

A) 25%

B) 20%

C) $33\frac{1}{3}%$

D) 15%

Answer

Correct Answer: A

$33\\frac{1}{3}\% = \\frac{1}{3}$. Price increases from 3 to 4. Expenditure = Price $\\times$ Consumption. To keep Exp constant, Consumption must be the inverse ratio. Consumption decreases from 4 to 3. Reduction = $(\\frac{4-3}{4}) \\times 100 = \\frac{1}{4} \\times 100 = 25\%$.

Question 16

16. In a library, 20% of books are in Hindi, 50% of the remaining are in English and 30% of the remaining are in French. If the rest of the 6,300 books are in Regional languages, find the total number of books in the library.

A) 18,000

B) 25,000

C) 22,500

D) 20,000

Answer

Correct Answer: C

Let total books be B. Remaining after Hindi = 0.80B. Remaining after English = $0.50 \\times 0.80B = 0.40B$. Remaining after French = $0.70 \\times 0.40B = 0.28B$. Given 0.28B = 6300. $B = \\frac{6300}{0.28} = \\frac{630000}{28} = 22500$.

Question 17

17. If the length of a rectangle is increased by 60%, by what percentage should the width be decreased to maintain the same area?

A) 40%

B) 37.5%

C) 35%

D) 60%

Answer

Correct Answer: B

Let length L and width W. Area A = LW. New length L' = 1.6L. New width W'. $1.6L \\times W' = LW \\Rightarrow W' = \\frac{W}{1.6} = 0.625W$. Decrease in width = $(1 - 0.625) \\times 100 = 37.5\%$.

Question 18

18. The price of an item is increased by x%. Later, the new price is decreased by x%. If the latest price is 1 Rupee, then the original price was:

A) 1

B) $\frac{1-x^2}{100}$

C) $\frac{100-x^2}{100}$

D) $\frac{10000}{10000 - x^2}$

Answer

Correct Answer: D

Let original price be P. Price after increase = $P(1 + \\frac{x}{100})$. Price after decrease = $P(1 + \\frac{x}{100})(1 - \\frac{x}{100}) = P(1 - \\frac{x^2}{10000})$. Given $P(1 - \\frac{x^2}{10000}) = 1$. $P(\\frac{10000 - x^2}{10000}) = 1 \\Rightarrow P = \\frac{10000}{10000 - x^2}$.

Question 19

19. A solution of salt and water contains 5% salt. If 20 liters of water are evaporated, the salt concentration becomes 15%. Find the initial quantity of the solution.

A) 30 liters

B) 25 liters

C) 40 liters

D) 35 liters

Answer

Correct Answer: A

Let initial volume be V. Salt = 0.05V. Final volume = V - 20. Salt = 0.15(V - 20). 0.05V = 0.15V - 3 0.10V = 3 \\Rightarrow V = 30 liters.

Question 20

20. A person spends 75% of his income. His income increases by 20% and his expenditure increases by 10%. What is the percentage increase in his savings?

A) 30%

B) 40%

C) 50%

D) 25%

Answer

Correct Answer: C

Let Income = 100, Expenditure = 75, Savings = 25. New Income = $100 \\times 1.20 = 120$. New Expenditure = $75 \\times 1.10 = 82.5$. New Savings = 120 - 82.5 = 37.5. Increase in Savings = 37.5 - 25 = 12.5. Percentage increase = $(\\frac{12.5}{25}) \\times 100 = 50\%$.

Accepted Answer

Correct Answer: A

Initial mass = 45 kg. Titanium = 35\% of 45 = $0.35 \\times 45 = 15.75$ kg. Nickel added = 15 kg. New total mass = 45 + 15 = 60 kg. New Titanium % = $(\\frac{15.75}{60}) \\times 100 = \\frac{1575}{60} = 26.25\%$.