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Percentage — Questions and Answers

Percentage is the foundation on which profit and loss, interest, data interpretation and population growth all sit. Converting percentages to fractions on sight (12.5% = 1/8, 16⅔% = 1/6, 6.25% = 1/16) is the single biggest speed upgrade available in any aptitude section — it turns three-line calculations into mental arithmetic.

28 solved questionsArithmetic AptitudeFree · no signup

Percentage— Concepts, Formulas & Shortcuts

  • x% of y = xy/100, and x% of y = y% of x (useful shortcut).
  • Learn the fraction table: 50% = 1/2, 33⅓% = 1/3, 25% = 1/4, 20% = 1/5, 16⅔% = 1/6, 12.5% = 1/8, 10% = 1/10, 6.25% = 1/16.
  • Increase by x% then decrease by x% ⇒ net change = −x²/100 % (always a decrease).
  • Successive changes of a% and b% ⇒ net = a + b + ab/100 percent (use signs).
  • If A is x% more than B, then B is 100x/(100 + x) % less than A.
  • Price rises by x% ⇒ consumption must fall by 100x/(100 + x) % to keep expenditure unchanged.

Percentage Practice Questions with Answers

Attempt each question first, then open the explanation. All 28 questions below are free to read and require no signup.

  1. Q1.What is 25% of 320?

    Easy
    • A70
    • B75
    • C80
    • D85
    +Show Answer & Explanation

    Answer: C. 80

    Explanation: 25% = 1/4, so 320/4 = 80.

    Percentage question 1 of 28

  2. Q2.If 40% of a number is 120, the number is:

    Easy
    • A240
    • B280
    • C300
    • D320
    +Show Answer & Explanation

    Answer: C. 300

    Explanation: Number = 120 × 100/40 = 300.

    Percentage question 2 of 28

  3. Q3.A number is increased by 20% and then decreased by 20%. The net change is:

    Moderate
    • ANo change
    • B4% increase
    • C4% decrease
    • D2% decrease
    +Show Answer & Explanation

    Answer: C. 4% decrease

    Explanation: 1.2 × 0.8 = 0.96, a 4% decrease. General rule: −x²/100 %.

    Percentage question 3 of 28

  4. Q4.A student scoring 30% failed by 30 marks, while another scoring 45% got 15 marks more than the pass mark. The maximum marks are:

    Difficult
    • A200
    • B250
    • C300
    • D350
    +Show Answer & Explanation

    Answer: C. 300

    Explanation: The 15% gap equals 30 + 15 = 45 marks → 15% of M = 45 → M = 300.

    Percentage question 4 of 28

  5. Q5.A salary is increased by 25%. By what per cent must it be reduced to bring it back to the original?

    Moderate
    • A15%
    • B20%
    • C22.5%
    • D25%
    +Show Answer & Explanation

    Answer: B. 20%

    Explanation: Reduction = 25/125 × 100 = 20%.

    Percentage question 5 of 28

  6. Q6.If the price of sugar rises by 25%, by how much per cent must a family reduce consumption to keep expenditure unchanged?

    Moderate
    • A15%
    • B18%
    • C20%
    • D25%
    +Show Answer & Explanation

    Answer: C. 20%

    Explanation: Reduction = 100 × 25/(100 + 25) = 20%.

    Percentage question 6 of 28

  7. Q7.Two numbers are respectively 20% and 50% more than a third number. The first as a percentage of the second is:

    Moderate
    • A75%
    • B80%
    • C85%
    • D90%
    +Show Answer & Explanation

    Answer: B. 80%

    Explanation: Take the third as 100 → first = 120, second = 150 → 120/150 × 100 = 80%.

    Percentage question 7 of 28

  8. Q8.In a school 70% of the students are boys and there are 504 girls. The total number of students is:

    Easy
    • A1,440
    • B1,560
    • C1,680
    • D1,720
    +Show Answer & Explanation

    Answer: C. 1,680

    Explanation: Girls = 30% = 504 → total = 504 × 100/30 = 1,680.

    Percentage question 8 of 28

  9. Q9.The population of a town grows 10% every year and is 26,620 after 3 years. Its original population was:

    Moderate
    • A18,000
    • B20,000
    • C22,000
    • D24,000
    +Show Answer & Explanation

    Answer: B. 20,000

    Explanation: P × 1.1³ = 26620 → P = 26620/1.331 = 20,000.

    Percentage question 9 of 28

  10. Q10.If x% of 250 is 50, then x is:

    Easy
    • A15
    • B20
    • C25
    • D30
    +Show Answer & Explanation

    Answer: B. 20

    Explanation: x = 50 × 100/250 = 20.

    Percentage question 10 of 28

  11. Q11.What is 15% of 400?

    Easy
    • A45
    • B50
    • C60
    • D75
    +Show Answer & Explanation

    Answer: C. 60

    Explanation: 15% of 400 = 0.15 × 400 = 60.

    Percentage question 11 of 28

  12. Q12.If 25% of a number is 75, the number is:

    Easy
    • A225
    • B250
    • C300
    • D375
    +Show Answer & Explanation

    Answer: C. 300

    Explanation: Number = 75 × 100/25 = 300.

    Percentage question 12 of 28

  13. Q13.A number is decreased by 25% and then increased by 25%. The net change is:

    Moderate
    • ANo change
    • B6.25% decrease
    • C6.25% increase
    • D12.5% decrease
    +Show Answer & Explanation

    Answer: B. 6.25% decrease

    Explanation: 0.75 × 1.25 = 0.9375, a 6.25% decrease. General rule: −x²/100 %.

    Percentage question 13 of 28

  14. Q14.In an election between two candidates, the winner got 60% of the votes and won by 1,200 votes. The total number of votes was:

    Moderate
    • A4,000
    • B5,000
    • C6,000
    • D8,000
    +Show Answer & Explanation

    Answer: C. 6,000

    Explanation: The margin is 60% − 40% = 20% of the total = 1,200 → total = 6,000 votes.

    Percentage question 14 of 28

  15. Q15.The price of an item is increased by 10% and then by another 20%. The total increase is:

    Moderate
    • A30%
    • B31%
    • C32%
    • D33%
    +Show Answer & Explanation

    Answer: C. 32%

    Explanation: 1.10 × 1.20 = 1.32, so the net increase is 32%.

    Percentage question 15 of 28

  16. Q16.A student scored 480 marks out of 600. His percentage is:

    Easy
    • A75%
    • B78%
    • C80%
    • D85%
    +Show Answer & Explanation

    Answer: C. 80%

    Explanation: 480/600 × 100 = 80%.

    Percentage question 16 of 28

  17. Q17.If A's income is 25% more than B's, then B's income is less than A's by:

    Moderate
    • A15%
    • B20%
    • C22%
    • D25%
    +Show Answer & Explanation

    Answer: B. 20%

    Explanation: Reduction = 100 × 25/(100 + 25) = 20%.

    Percentage question 17 of 28

  18. Q18.60% of the students in a class are girls. If there are 24 boys, the total strength is:

    Easy
    • A48
    • B56
    • C60
    • D72
    +Show Answer & Explanation

    Answer: C. 60

    Explanation: Boys = 40% = 24 → total = 24 × 100/40 = 60 students.

    Percentage question 18 of 28

  19. Q19.The salary of an employee is reduced by 20% and later increased by 25%. His new salary compared with the original is:

    Moderate
    • A5% less
    • Bthe same
    • C5% more
    • D10% less
    +Show Answer & Explanation

    Answer: B. the same

    Explanation: 0.80 × 1.25 = 1.00, so the salary returns exactly to the original.

    Percentage question 19 of 28

  20. Q20.If the length of a rectangle is increased by 50%, by what per cent must the breadth be reduced to keep the area unchanged?

    Difficult
    • A25%
    • B30%
    • C33 1/3%
    • D50%
    +Show Answer & Explanation

    Answer: C. 33 1/3%

    Explanation: Reduction = 100 × 50/(100 + 50) = 33⅓%.

    Percentage question 20 of 28

  21. Q21.What is 20% of 750?

    Easy
    • A120
    • B140
    • C150
    • D160
    +Show Answer & Explanation

    Answer: C. 150

    Explanation: 0.20 × 750 = 150.

    Percentage question 21 of 28

  22. Q22.If 60% of a number is 240, the number is:

    Easy
    • A360
    • B380
    • C400
    • D420
    +Show Answer & Explanation

    Answer: C. 400

    Explanation: Number = 240 × 100/60 = 400.

    Percentage question 22 of 28

  23. Q23.45 is what percentage of 180?

    Easy
    • A20%
    • B25%
    • C30%
    • D35%
    +Show Answer & Explanation

    Answer: B. 25%

    Explanation: 45/180 × 100 = 25%.

    Percentage question 23 of 28

  24. Q24.A number increased by 30% becomes 260. The original number is:

    Moderate
    • A180
    • B190
    • C200
    • D210
    +Show Answer & Explanation

    Answer: C. 200

    Explanation: 1.30x = 260 → x = 200.

    Percentage question 24 of 28

  25. Q25.The price of a shirt falls from ₹800 to ₹680. The percentage decrease is:

    Easy
    • A12%
    • B15%
    • C18%
    • D20%
    +Show Answer & Explanation

    Answer: B. 15%

    Explanation: Decrease = ₹120 on ₹800 → 120/800 × 100 = 15%.

    Percentage question 25 of 28

  26. Q26.In a class of 80, 25% failed. The number who passed is:

    Easy
    • A55
    • B58
    • C60
    • D65
    +Show Answer & Explanation

    Answer: C. 60

    Explanation: Passed = 75% of 80 = 60 students.

    Percentage question 26 of 28

  27. Q27.If a number is first increased by 10% and then by 10% again, the total increase is:

    Moderate
    • A20%
    • B21%
    • C22%
    • D25%
    +Show Answer & Explanation

    Answer: B. 21%

    Explanation: 1.1 × 1.1 = 1.21, so the increase is 21%.

    Percentage question 27 of 28

  28. Q28.A candidate scoring 40% fails by 20 marks, while the pass mark is 45% of the maximum. The maximum marks are:

    Difficult
    • A300
    • B350
    • C400
    • D450
    +Show Answer & Explanation

    Answer: C. 400

    Explanation: The 5% gap equals 20 marks → 5% of M = 20 → M = 400.

    Percentage question 28 of 28

Percentage — Frequently Asked Questions

If my salary is cut 20% then raised 20%, do I get back to the original?+

No. The net effect is a 4% decrease, because the 20% rise is applied to a smaller base. The general result is −x²/100 %.

How do I convert a percentage to a fraction quickly?+

Memorise the standard table up to 1/16. In exams, 37.5% instantly becoming 3/8 saves more time than any other single shortcut.

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