Competitive Exams : Quantitative Aptitude - Percentage (Set 6) | Concept of Maths

Question 1

1. The price of a rare isotope increased by 25% in 2024, decreased by 20% in 2025, and then increased by 15% in 2026. If the final price at the end of 2026 is $\13,800, what was the price at the beginning of 2024?

A) $\10,000

B) $\11,500

C) $\12,000

D) $\12,500

Answer

Correct Answer: C

Let the initial price be P. Successive changes: $P \\\times 1.25 \\\times 0.80 \\\times 1.15 = 13800$. Note: $1.25 \\\times 0.80 = 1$. So, $P \\\times 1 \\\times 1.15 = 13800 \\⇒ P = \\\frac{13800}{1.15} = 12000$.

Question 2

2. In a text-based efficiency graph, Cell A shows 80%, Cell B 90%, Cell C 75%, and Cell D 85%. If Cell B's energy output is 540 kW, find the combined output of Cells A and C.

A) 900 kW

B) 930 kW

C) 950 kW

D) 980 kW

Answer

Correct Answer: B

Cell B (90%) = 540 kW. 1% efficiency = \\rac{540}{90} = 6 kW. Output A (80%) = $80 \\\times 6 = 480$ kW. Output C (75%) = $75 \\\times 6 = 450$ kW. Total = 480 + 450 = 930 kW.

Question 3

3. In an intergalactic election between two candidates, 20% of the votes were declared invalid. Candidate X secured 60% of the valid votes and won by a margin of 3,200 votes. How many total votes were cast?

A) 20,000

B) 25,000

C) 18,000

D) 22,500

Answer

Correct Answer: A

Let total votes be V. Valid votes = 0.80V. Candidate X = 60% of 0.80V, Candidate Y = 40% of 0.80V. Difference = (60% - 40%) of $0.80V = 0.20 \\\times 0.80V = 0.16V$. $0.16V = 3200 \\⇒ V = \\\frac{3200}{0.16} = 20,000$.

Question 4

4. The price of Helium-3 fusion fuel increases by 20%. By what percentage must a reactor technician reduce the consumption so that the total expenditure increases by only 5%?

A) 10%

B) 12%

C) 15%

D) 12.5%

Answer

Correct Answer: D

Expenditure = Price \\ imes Consumption. $1.05 = 1.20 \\\times (1 - r)$. $1 - r = \\\frac{1.05}{1.20} = \\\frac{105}{120} = \\\frac{7}{8} = 0.875$. r = 1 - 0.875 = 0.125 or 12.5%.

Question 5

5. The population of a Martian colony increases by 10% annually. At the end of every year, 5% of the updated population migrates back to Earth. If the initial population was 10,000, what is the population at the end of 2 years?

A) 10,900

B) 10,920

C) 10,920.25 (rounded to 10,920)

D) 11,000

Answer

Correct Answer: C

Year 1 start: 10,000. Growth: 11,000. After migration (95%): $11,000 \\\times 0.95 = 10,450$. Year 2 start: 10,450. Growth (+10%): $10,450 \\\times 1.1 = 11,495$. After migration (95%): $11,495 \\\times 0.95 = 10,920.25$.

Question 6

6. A cybersecurity firm allocates 30% of its budget to Hardware. Of the remaining, 40% is spent on Software and 25% on Research. The rest, $\1,470,000, is for Salaries. Find the total budget.

A) $\6,000,000

B) $\5,500,000

C) $\7,200,000

D) $\4,800,000

Answer

Correct Answer: A

Remaining after Hardware: 100% - 30% = 70%. Spent from remaining: 40% + 25% = 65%. Left for Salaries: 100% - 65% = 35% of the remaining 70%. $0.35 \\\times 0.70 \\\times Total = 1,470,000$. $0.245 \\\times Total = 1,470,000 \\⇒ Total = \\\frac{1,470,000}{0.245} = 6,000,000$.

Question 7

7. In a Neuro-sync certification, a candidate must score 40% to pass. Candidate Alpha scored 178 marks and failed by 22 marks. What were the maximum possible marks?

A) 450

B) 500

C) 550

D) 600

Answer

Correct Answer: B

Passing marks = 178 + 22 = 200. 40% of Max Marks = 200. Max Marks = \\rac{200}{0.40} = 500.

Question 8

8. An android salesperson earns a 5% commission on sales up to \20,000 and 8% on sales exceeding that amount. If the total commission earned is\2,600, what were the total sales?

A) $\35,000

B) $\38,000

C) $\42,000

D) $\40,000

Answer

Correct Answer: D

Commission on first \20,000 = 0.05 \\\times 20,000 = 1,000. Remaining commission =2,600 - 1,000 = 1,600. Let extra sales beX.0.08X = 1,600 \\⇒ X = 20,000. Total sales =20,000 + 20,000 = 40,000$.

Question 9

9. Solution X contains 10% acid and Solution Y contains 30% acid. In what ratio should X and Y be mixed to obtain a solution with 25% acid?

A) 1:2

B) 2:1

C) 1:3

D) 3:1

Answer

Correct Answer: C

Using Alligation: (Higher % - Mean %) : (Mean % - Lower %) (30 - 25) : (25 - 10) = 5 : 15 = 1 : 3.

Question 10

10. A mining drone depreciates in value by 10% every year. If its current value is $\72,900, what was its value 3 years ago?

A) $\100,000

B) $\90,000

C) $\110,000

D) $\95,000

Answer

Correct Answer: A

Let initial value be V. $V \\\times (0.9)^3 = 72,900$. $V \\\times 0.729 = 72,900 \\⇒ V = 100,000$.

Question 11

11. The data throughput of Server A is 25% more than Server B. By what percentage is Server B's throughput less than Server A?

A) 25%

B) 20%

C) 15%

D) 22.5%

Answer

Correct Answer: B

Let B = 100. Then A = 125. Difference = 25. Percentage less = $\\rac{25}{125} \\\times 100 = 20%$.

Question 12

12. Asteroid mining profits are taxed at 5% for the first \1 million and 12% for any amount above that. If a company paid\290,000 in taxes, what was their total profit?

A) $\2,500,000

B) $\3,200,000

C) $\2,800,000

D) $\3,000,000

Answer

Correct Answer: D

Tax on first \1M = 0.05 \\\times 1,000,000 = 50,000. Remaining tax =290,000 - 50,000 = 240,000. Let profit above\1M be P. 0.12P = 240,000 \\⇒ P = 2,000,000. Total profit = 1,000,000 + 2,000,000 = 3,000,000.

Question 13

13. In a survey of 500 astronauts, 60% have visited the Moon, 50% have visited Mars, and 20% have visited both. How many have visited neither?

A) 40

B) 50

C) 60

D) 100

Answer

Correct Answer: B

Total visiting at least one = n(Moon) + n(Mars) - n(Both) = 60% + 50% - 20% = 90%. Neither = 100% - 90% = 10%. 10% of 500 = 50.

Question 14

14. For a gas in a container, if the pressure is increased by 20% and the absolute temperature is increased by 50%, by what percentage does the volume change? (Use PV = nRT)

A) Increases by 25%

B) Increases by 30%

C) Decreases by 20%

D) Remains same

Answer

Correct Answer: A

$V \\\propto \\\frac{T}{P}$. New Volume $V' = \\\frac{1.5T}{1.2P} = 1.25 \\\frac{T}{P}$. Change = 1.25 - 1 = 0.25 or 25% increase.

Question 15

15. A high-precision sensor's error margin was x%. After an upgrade, it decreased by x%, resulting in a final error margin that was 16% less than the original. Find x.

A) 20

B) 30

C) 40

D) 25

Answer

Correct Answer: C

Let original margin be M. After decrease: $M(1 - \\\frac{x}{100})$. But the problem states the decrease itself was x% of the value. Actually, standard successive logic: $M \\\times (1 - \\\frac{x}{100}) = M \\\times 0.84$ (not applicable). If it means x percent of x percent: $x - \\\frac{x^2}{100} = \\no$. Correct Interpretation: The "decrease by x%" leads to $1 - (x/100)^2$ logic for successive. If it's a single change: x = 16. Let's look at the wording: "decreased by x%". If final is 84% of original, then x=16. However, if it's a two-stage reduction of x and x (successive): $(1-x/100)^2 = 0.84$ (not clean). Let's assume the question implies: x% of x = 16. Then $x^2/100 = 16 \\⇒ x = 40$.

Question 16

16. A Hyperloop ticket costs $\200. When the price was reduced by 20%, the number of passengers increased by 40%. What is the net change in daily revenue?

A) 10% decrease

B) 12% increase

C) 8% increase

D) 15% increase

Answer

Correct Answer: B

Revenue = Price \\ imes Passengers. Net change = $(0.80 \\\times 1.40) - 1 = 1.12 - 1 = 0.12$. 12% increase.

Question 17

17. A nanobot factory has two lines. Line A produces 60% of the output with 2% defects. Line B produces 40% of the output with 5% defects. What is the overall defect percentage?

A) 3.2%

B) 3.5%

C) 3.8%

D) 4.0%

Answer

Correct Answer: A

Overall defect = $(0.60 \\\times 0.02) + (0.40 \\\times 0.05)$ = 0.012 + 0.020 = 0.032 = 3.2%.

Question 18

18. The salary of a tech lead is first increased by 10% and then decreased by 10%. If the final salary is $\19,800, what was the original salary?

A) $\19,800

B) $\19,900

C) $\20,000

D) $\21,000

Answer

Correct Answer: C

Successive change: $1.10 \\\times 0.90 = 0.99$ (a 1% net decrease). $0.99 \\\times S = 19,800$. $S = \\\frac{19,800}{0.99} = 20,000$.

Question 19

19. In a space station, 40% of the crew are Engineers, 30% are Scientists, and the remaining 150 are Security. If 20% of Engineers are on leave, how many Engineers are currently working?

A) 150

B) 200

C) 180

D) 160

Answer

Correct Answer: D

Security % = 100% - (40% + 30%) = 30%. 30% = 150 \\⇒ 1% = 5. Total Engineers = $40 \\\times 5 = 200$. Working Engineers (80%) = $200 \\\times 0.8 = 160$.

Question 20

20. A trader sells a gadget at a profit of 20%. Had he bought it for 10% less and sold it for $\30 less, he would have gained 20%. What was the original cost price?

A) $\200

B) $\250

C) $\300

D) $\400

Answer

Correct Answer: B

Let CP = 100x, SP = 120x. New CP = 90x, New SP = 120x - 30. Profit % = $\\rac{(120x - 30) - 90x}{90x} \\\times 100 = 20$. \\rac{30x - 30}{90x} = 0.2 \\⇒ 30x - 30 = 18x. 12x = 30 \\⇒ x = 2.5. CP = $100 \\\times 2.5 = 250$.