Percentage: 20 mixed-difficulty Percentage problems- each with step-by-step (digit-by-digit) solutions

Percentage: 20 mixed-difficulty Percentage problems– each with step-by-step (digit-by-digit) solutions

Percentage Questions

Basic Level

1. Convert 3/4 into a percentage.
2. Express 45% as a fraction in simplest form.
3. Find 25% of 360.
4. A student scores 120 marks out of 150. Find his percentage.
5. If 15% of a number is 45, find the number.

Moderate Level

6. The price of a pen increases from ₹40 to ₹50. Find the percentage increase.
7. The population of a town decreases from 25,000 to 20,000. Find the percentage decrease.
8. A shopkeeper marks an item at ₹500 and sells it for ₹400. Find the discount percentage.
9. A man spends 65% of his income. If his income is ₹20,000, how much does he save?
10. The price of a shirt was ₹800. A shopkeeper gives 10% discount and then 20% discount on the reduced price. Find the selling price.

Applied Level

11. A man’s salary is increased by 20% and then reduced by 20%. Find the net percentage change.
12. Out of 2000 voters, 60% are men. 80% of men and 70% of women voted. Find the percentage of total voters who voted.
13. A student scored 40% marks and failed by 20 marks. If passing marks are 120, find the maximum marks.
14. A price of sugar rises by 25%. By what percent must a family reduce its consumption so that expenditure remains the same?
15. The population of a town increases by 10% in the first year and 20% in the next year. Find the net % increase.

Exam-Level (Tricky)

16. A man spends 80% of his income. If his income increases by 25% and his expenditure increases by 20%, by what % do his savings increase?
17. A candidate got 40% of total votes and lost by 200 votes. Find the total number of votes.
18. The price of a book is reduced by 20% to ₹480. What was its original price?
19. The population of a city was 50,000. It increased by 10% in the first year, and again by 10% in the second year. Find the population after 2 years.
20. A man gives 40% of his money to his wife, 20% to his son, and 10% to charity. He is left with ₹18,000. Find his original amount.

step-by-step solutions  for all 20 percentage questions. I show the arithmetic clearly so you can follow every small step.

Step-by-step solutions — 20 Percentage Problems

1. Convert 3/4​ into a percentage.
   Solution: 3/4×100=0.75×100=75%

Answer: 75%

2. Express 45% as a fraction (simplest form).
   Solution: 45%=45/100   Divide numerator & denominator by 5: (45÷5)/(100÷5) =9/20 .
   Answer: 9/20

3. Find 25% of 360.
   Solution: 25%=25/100=0.25 .

0.25×360=25/100×360=25×360/100.

Compute: 25×360=25×(36×10)=900×10=9000 

Then 9000÷100=90.
Answer: 90

4. A student scores 120 marks out of 150. Find his percentage.
   Solution: 120/150×100

 Simplify fraction: 120/150=12/15=4/5=0.8
So 0.8×100=80%.
Answer: 80%

5. If 15% of a number is 45, find the number.
   Solution: Let number = x. Then 15/100 x=45. So x=45×100/15​.
   Compute 100/15=20/3 

Then 45×20/3=45÷3×20=15×20=300

Answer: 300

6. Price increases from ₹40 to ₹50. Find percentage increase.
   Solution: Increase = 50−40=10 

Percentage increase =10/40×100
10/40=1/4=0.25

So 0.25×100=25%.
Answer: 25%

7. Population decreases from 25,000 to 20,000. Find percentage decrease.
   Solution: Decrease = 25000−20000=5000

Percentage decrease =5000/25000×100.
5000/25000=1/5=0.2

So 0.2×100=20%
Answer: 20%

8. Marked price ₹500, sold at ₹400. Find discount percentage.
   Solution: Discount = 500−400=100

Discount% =100/500×100
100/500=1/5=0.2

So 0.2×100=20%0.2
Answer: 20%

9. A man spends 65% of income. If income is ₹20,000, how much does he save?
   Solution: Spending = 65% ,  so saving% = 100%−65%=35%
   Savings = 35%×20000=35/100×20000

Compute: 20000÷100=200

200×35=7000
Answer: ₹7,000

10. Shirt priced ₹800. 10% discount, then 20% discount on reduced price. Find final price.
    Solution: First discount 10% of 800 = 0.10×800=80

Price after 1st discount = 800−80=720 .
Second discount 20% of 720 = 0.20×720=144

Final price = 720−144=576.
Answer: ₹576

11. Salary +20% then −20%. Net percentage change?
    Solution (use numbers): Start with 100. After +20% → 100×1.20=120

After −20% → reduce 20% of 120 = 0.20×120=240

So new = 120−24=96
Net change = 96−100=−4 → net decrease of 4%

Answer: Net decrease 4%

12. 2000 voters: 60% men. 80% of men and 70% of women voted. Percentage of total voters who voted?
    Solution: Men = 60% of 2000 = 0.6×2000=1200 

 Women = 2000−1200=800
Men who voted = 80% of 1200 = 0.8×1200=960
Women who voted = 70% of 800 = 0.7×800=560
Total voted = 960+560=1520

Percentage = 1520/2000×100=0.76×100=76%

Answer: 76%

13. Student scored 40% and failed by 20 marks. Passing marks = 120. Find maximum marks.
    Solution: If failed by 20, student’s score = 120−20=100

This is 40% of total marks M: 0.40M=100

So M=100/0.40=250
(Alternatively 100×100/40=250)
Answer: 250 (maximum marks)

14. Price of sugar rises 25%. By what percent must consumption be reduced so expenditure remains same?
    Solution: Let original price =P

Original consumption =C,

Original expenditure =P×C

New price =1.25P=1.25P=1.25P.

Need new consumption C with 1.25P×C′=P×C

So C′=C/1.25=0.8C

Reduction =C−C′=0.2C

Percentage reduction =0.2C/C×100=20%.
Answer: 20%

15. Population increases 10% first year, then 20% next year. Net % increase?
    Solution: Use multiplication: Combined factor =1.10×1.20=1.32

Net increase factor =1.32−1=0.32

So net increase =0.32×100=32%
Answer: 32%

16. A man spends 80% of income. Income ↑25% and expenditure ↑20%. By what % do his savings increase?
    Solution: Let initial income = x.

Initial expenditure = 0.80x

Initial savings = I−0.80I=0.20x.
New income = 1.25x.

New expenditure = 0.80x×1.20=0.96x

New savings = 1.25x−0.96x=0.29x.
Increase in savings = 0.29x−0.20x=0.09x

Percentage increase relative to old savings = 0.09x/0.20x×100=0.09/0.20×100=0.45×100=45

Answer: Savings increase by 45%

17. Candidate got 40% of total votes and lost by 200 votes. Find total votes.
    Solution & assumption: typically this problem assumes only two candidates. Then winner has 60% and loser 40%.

Difference = 60%−40%=20% of total votes.

So 20% of total =200

That is 20/100V=200 ⇒ 0.20V=200 ⇒ V=200/0.20=1000
Answer: 1000 total votes
(If more than two candidates, extra info would be needed; above uses the standard two-candidate assumption.)

18. Price reduced by 20% to ₹480. Find original price.
    Solution: If original price =X, after 20% reduction new price =0.80X=480

So X=480÷0.8

Compute 480÷0.8=480×10/8=480×1.25=600.
Answer: ₹600

19. Population 50,000; +10% first year, +10% second year. Find population after 2 years.
    Solution: Multiply by 1.10 twice: 50000×1.10×1.10=50000×1.21

Compute 50000×1.21=50000+0.21×50000=50000+10500=60500
Answer: 60,500

20. Man gives 40% to wife, 20% to son, 10% to charity. Left with ₹18,000. Find original amount.
    Solution: Total given = 40%+20%+10%=70%

So left = 100%−70%=30%

So 30% of original = 18000 ⇒ 0.30×X=180000.

Thus X=18000÷0.30=18000×100/30=18000×10/3=60000
Answer: ₹60,000