Competitive Exams : Quantitative Aptitude - Percentage (Set 10) | Concept of Maths

Question 1

1. In a quantum simulation, the energy of a particle increases by 24% in the first epoch and decreases by 15% in the second. If the resultant energy is 474.3 Joules, what was the initial energy level?

A) 450 Joules

B) 465 Joules

C) 440 Joules

D) 480 Joules

Answer

Correct Answer: A

\nLet initial energy be E. \\nAfter 1st epoch: $E \\times (1 + 0.24) = 1.24E$. \\nAfter 2nd epoch: $1.24E \\times (1 - 0.15) = 1.24E \\times 0.85 = 1.054E$. \\nGiven 1.054E = 474.3. \\n$E = \\frac{474.3}{1.054} = 450$. \\nCorrect Answer: 450 Joules.\n

Question 2

2. In a tripartite election in Ranchi, Candidate A secured 42% of the valid votes. 15% of total votes were invalid. Candidate B secured 30% of the valid votes. If the total votes polled were 5,00,000, find the number of votes secured by Candidate C.

A) 1,27,500

B) 1,78,500

C) 1,19,000

D) 1,45,000

Answer

Correct Answer: C

\nTotal votes = 5,00,000. \\nValid votes = $5,00,000 \\times 0.85 = 4,25,000$. \\nValid votes % for C = 100% - (42% + 30%) = 28%. \\nVotes for C = $0.28 \\times 4,25,000 = 1,19,000$. \\nCorrect Answer: 1,19,000.\n

Question 3

3. A manufacturing unit reports that raw material costs comprise 60% of the total production cost. If the price of raw materials rises by 25% and the labor cost (which accounts for 30% of total) rises by 40%, with other costs remaining constant, what is the net percentage increase in total production cost?

A) 24%

B) 27%

C) 21.5%

D) 30%

Question 4

4. A student requires 40% marks to pass an exam. He gets 178 marks and fails by 22 marks. What is the maximum marks possible for the examination?

A) 400

B) 450

C) 600

D) 500

Answer

Correct Answer: D

\nPassing marks = 178 + 22 = 200. \\nGiven 40% of Maximum Marks (M) = 200. \\n$0.4M = 200 \\Rightarrow M = \\frac{200}{0.4} = 500$. \\nCorrect Answer: 500.\n

Question 5

5. If the price of aviation turbine fuel increases by $33 \\frac{1}{3}%$, by what percentage must an airline reduce its fuel consumption so that the total expenditure remains the same?

A) 25%

B) 33.33%

C) 20%

D) 16.67%

Answer

Correct Answer: A

\nIncrease = $33 \\frac{1}{3}% = \\frac{1}{3}$. \\nFormula for reduction: $\\frac{r}{100+r} \\times 100$. \\nOr using fractions: If price becomes $\\frac{4}{3}$, consumption must become $\\frac{3}{4}$ to keep product constant. \\nReduction = $1 - \\frac{3}{4} = \\frac{1}{4} = 25%$. \\nCorrect Answer: 25%.\n

Question 6

6. Fresh watermelons contain 92% water. After being stored in a dry warehouse for 5 days, they contain 80% water. If the original weight of watermelons was 500 kg, what is their weight now?

A) 250 kg

B) 100 kg

C) 200 kg

D) 300 kg

Answer

Correct Answer: C

\nWeight of dry pulp remains constant. \\nInitial pulp = 8% of 500 = 40 kg. \\nIn stored watermelons, water is 80%, so pulp is 20%. \\nLet new weight be W. 20% of W = 40. \\n0.2W = 40 \\Rightarrow W = 200 kg. \\nCorrect Answer: 200 kg.\n

Question 7

7. In a competitive survey in Ranchi, 65% of people like Product A, 72% like Product B, and 15% like neither. If 4,160 people like both products, how many people were surveyed in total?

A) 7,500

B) 8,000

C) 10,000

D) 6,400

Answer

Correct Answer: B

\nPercentage liking at least one product = 100% - 15% = 85%. \\nLet x be % liking both. $n(A \\cup B) = n(A) + n(B) - n(A \\cap B)$. \\n85 = 65 + 72 - x \\Rightarrow x = 137 - 85 = 52%. \\nGiven 52% of Total (T) = 4,160. \\n$0.52T = 4,160 \\Rightarrow T = \\frac{4,160}{0.52} = 8,000$. \\nCorrect Answer: 8,000.\n

Question 8

8. A man's annual income increases by Rs. 2.6 Lakhs, but the tax on income he has to pay reduced from 15% to 12%. He now pays the same amount of tax as before. What is his increased income?

A) Rs. 13 Lakhs

B) Rs. 10.4 Lakhs

C) Rs. 15.6 Lakhs

D) Rs. 12 Lakhs

Answer

Correct Answer: A

\nLet initial income be I. New income = I + 2.6. \\nTax 1 = 0.15I. Tax 2 = 0.12(I + 2.6). \\n0.15I = 0.12I + 0.312. \\n0.03I = 0.312 \\Rightarrow I = 10.4. \\nIncreased income = 10.4 + 2.6 = 13 Lakhs. \\nCorrect Answer: Rs. 13 Lakhs.\n

Question 9

9. The population of a city increases at the rate of 5% annually. If its present population is 1,85,220, what was its population 3 years ago?

A) 1,70,000

B) 1,50,000

C) 1,65,000

D) 1,60,000

Answer

Correct Answer: D

\n$P_{now} = P_{old} \\times (1 + r/100)^n$. \\n$1,85,220 = P \\times (1.05)^3 = P \\times (\\frac{21}{20})^3$. \\n$1,85,220 = P \\times \\frac{9261}{8000}$. \\n$P = \\frac{1,85,220 \\times 8000}{9261} = 20 \\times 8000 = 1,60,000$. \\nCorrect Answer: 1,60,000.\n

Question 10

10. An alloy contains 32% copper, 24% zinc and the rest is nickel. How much nickel is present in 15.5 kg of the alloy?

A) 7.22 kg

B) 6.82 kg

C) 5.50 kg

D) 8.15 kg

Answer

Correct Answer: B

\nNickel % = 100% - (32% + 24%) = 44%. \\nWeight of Nickel = 44% of $15.5 = 0.44 \\times 15.5 = 6.82$ kg. \\nCorrect Answer: 6.82 kg.\n

Question 11

11. In a certain high school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years age, which is 48. What is the total number of students?

A) 80

B) 120

C) 100

D) 150

Answer

Correct Answer: C

\nStudents of 8 years = 48. \\nStudents above 8 years = $\\frac{2}{3} \\times 48 = 32$. \\nTotal students $\\ge 8$ years = 48 + 32 = 80. \\nSince 20% are below 8, 80% are $\\ge 8$ years. \\n0.8T = 80 \\Rightarrow T = 100. \\nCorrect Answer: 100.\n

Question 12

12. A reduction of 21% in the price of wheat enables a person to buy 10.5 kg more for Rs. 100. What is the reduced price per kg?

A) Rs. 2.00

B) Rs. 2.50

C) Rs. 3.00

D) Rs. 1.80

Answer

Correct Answer: A

\nSavings due to reduction = 21% of Rs. 100 = Rs. 21. \\nThis Rs. 21 allows buying 10.5 kg at the new price. \\nNew price = $\\frac{21}{10.5} = Rs. 2$ per kg. \\nCorrect Answer: Rs. 2.00.\n

Question 13

13. If A is 25% more than B, B is 20% less than C, and C is 30% more than D, then A is what percentage more or less than D?

A) 25% more

B) 10% less

C) 4% less

D) 30% more

Answer

Correct Answer: D

\nA = 1.25B, B = 0.8C, C = 1.3D. \\n$A = 1.25 \\times (0.8 \\times (1.3D)) = (1.25 \\times 0.8) \\times 1.3D = 1.0 \\times 1.3D = 1.3D$. \\nA is 30% more than D. \\nCorrect Answer: 30% more.\n

Question 14

14. A solution contains 18% salt. If 25 kg of water is evaporated, the salt concentration becomes 24%. Find the initial weight of the solution.

A) 80 kg

B) 100 kg

C) 120 kg

D) 75 kg

Answer

Correct Answer: B

\nSalt weight is constant. \\n$0.18 \\times W_{initial} = 0.24 \\times (W_{initial} - 25)$. \\n18W = 24W - 600 \\Rightarrow 6W = 600 \\Rightarrow W = 100 kg. \\nCorrect Answer: 100 kg.\n

Question 15

15. The price of an object is first increased by x% and then decreased by x%. If the final price is Rs. 1 and the net decrease is Rs. 0.04, find the value of x.

A) 20%

B) 10%

C) 15%

D) 25%

Answer

Correct Answer: A

\nNet change = $-\\frac{x^2}{100}%$. \\nInitial price (P) - Final price (1) = 0.04 \\Rightarrow P = 1.04. \\nNet % decrease = $\\frac{0.04}{1.04} \\times 100 \\approx 3.846%$. \\n$\\frac{x^2}{100} = 4 \\Rightarrow x^2 = 400 \\Rightarrow x = 20$. \\nCheck: $1.04 \\times (1 - \\frac{400}{10000}) = 1.04 \\times 0.96 = 0.9984 \\approx 1$. \\nCorrect Answer: 20%.\n

Question 16

16. In a library, 40% of the books are in Hindi, 60% of the remaining are in English and the rest of the books are in regional languages. If there are 4,800 books in English, what is the total number of books?

A) 15,000

B) 12,000

C) 20,000

D) 18,000

Answer

Correct Answer: C

\nLet total books be T. \\nRemaining after Hindi = 0.6T. \\nEnglish books = 60% of 0.6T = 0.36T. \\n$0.36T = 4,800 \\Rightarrow T = \\frac{4,800}{0.36} = 20,000$. \\nCorrect Answer: 20,000.\n

Question 17

17. If the radius of a sphere is increased by 50%, what is the percentage increase in its surface area?

A) 100%

B) 125%

C) 150%

D) 225%

Answer

Correct Answer: B

\nSurface area $A \\propto r^2$. \\nIf r becomes 1.5r, A becomes $(1.5)^2 A = 2.25A$. \\nIncrease = 2.25A - A = 1.25A = 125%. \\nCorrect Answer: 125%.\n

Question 18

18. A spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. His savings are increased by:

A) 10%

B) 25%

C) 33.33%

D) 50%

Answer

Correct Answer: D

\nInitial: Income=100, Exp=75, Sav=25. \\nNew: Income=120, Exp= $75 \\times 1.1 = 82.5$. \\nNew Sav = 120 - 82.5 = 37.5. \\nIncrease in Sav = 37.5 - 25 = 12.5. \\n% Increase = $\\frac{12.5}{25} \\times 100 = 50%$. \\nCorrect Answer: 50%.\n

Question 19

19. 40% of (A+B) = 60% of (A-B). Then $\\frac{2A-3B}{A+B}$ is:

A) 7/6

B) 5/6

C) 1/2

D) 2/3

Answer

Correct Answer: A

\n0.4(A+B) = 0.6(A-B) \\Rightarrow 2A + 2B = 3A - 3B \\Rightarrow A = 5B. \\nSubstitute A=5B: $\\frac{2(5B)-3B}{5B+B} = \\frac{10B-3B}{6B} = \\frac{7B}{6B} = \\frac{7}{6}$. \\nCorrect Answer: 7/6.\n

Question 20

20. A Sankey diagram of a hydroelectric plant shows: 100% Input, 20% lost in friction, 30% of the remaining lost in generator inefficiency, and 10% of that remainder lost in transmission. What percentage of the initial energy reaches the consumer?

A) 40%

B) 44%

C) 50.4%

D) 56%

Answer

Correct Answer: C

\nInitial = 100. \\nAfter friction: 100 - 20 = 80. \\nAfter generator: $80 - (0.3 \\times 80) = 80 - 24 = 56$. \\nAfter transmission: $56 - (0.1 \\times 56) = 56 - 5.6 = 50.4$. \\nCorrect Answer: 50.4%.\n