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100 Advanced Percentage Problems for Bank & Govt Exams

Master percentage concepts with 100 practice problems, shortcuts, and formulas for bank and competitive exams. Includes profit, loss, and population growth.

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100 Advanced Percentage Problems

A focused, exam-ready practice set for bank and competitive exams. Master core concepts, powerful shortcuts, and the most important problem types — all in one streamlined guide.

BANK EXAM PREP CORE FORMULAS SHORTCUTS PRACTICE SET
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Core Ideas of Percentages

Master these three foundational principles before solving any percentage problem.

1

The Concept of 100

A percentage is a fraction with 100 as its denominator. The Base Value (Original Number, Cost Price, Total Marks) is always 100%.

2

The 1% Method

Find 1% first, then scale up.

If 18% = 72
1% = 72 ÷ 18 = 4
Total (100%) = 4 × 100 = 400
3

Decimal Multipliers

Increase by 20% × 1.20
Decrease by 25% × 0.75
Increase by x% × (1 + x/100)
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Core Formulas

Recap & Review

Basic Calculations

% Value (Percentage ÷ 100) × Total
Ex 20% of 150 = 30
% Share (Part ÷ Whole) × 100
Ex 25 out of 200 = 12.5%
Original from % (Given Value × 100) ÷ Given %
Ex 40 is 8% of what? = 500
Increase [(New − Old) ÷ Old] × 100
Ex 60 to 75 = 25%
Decrease [(Old − New) ÷ Old] × 100
Ex 80 to 68 = 15%
Original after increase New ÷ (1 + r/100)
Ex 120 ÷ 1.2 = 100
Original after decrease New ÷ (1 − r/100)
Ex 75 ÷ 0.75 = 100

Profit, Loss & Discount

Profit% (Profit ÷ CP) × 100
Loss% (Loss ÷ CP) × 100
SP after Discount MP × (100 − Discount%) ÷ 100

Population Growth

After n years P × (1 + r/100)ⁿ
n years ago P ÷ (1 + r/100)ⁿ
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Easy Shortcuts

PERCENTAGE & APTITUDE FORMULAS

Net Change (Successive Changes)

Two changes x% and y%:
Net = x + y + (xy/100)

Use (+) for increase, (−) for decrease.
Example: 10% increase then 5% decrease = 4.5% increase.

Equivalent Single Discount

Two discounts d₁% and d₂%:
d₁ + d₂ − (d₁×d₂)/100
Example: 20% and 10% → 28%.

More Than / Less Than

A is x% more than B
→ B is less than A by x/(100+x) × 100
A is x% less than B
→ B is more than A by x/(100−x) × 100
Example: A is 25% more than B → B is 20% less than A.

Price & Consumption (Constant Expenditure)

Price ↑ r%
→ Consumption ↓ by r/(100+r) × 100
Price ↓ r%
→ Consumption ↑ by r/(100−r) × 100
Example: Price rises 20% → Consumption must fall 16.67%.

Equal Increase & Decrease

Increase by x% then decrease by x%
→ Always net decrease of x²/100 %
Example: 10% up then 10% down = 1% net decrease.

Exam Marks Shortcut

Total Marks =
(Failed by + Above pass)Difference in %
× 100
Example: fails by 12, above pass 18, differ 6% → total = 500.
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Practice Set: Percentage Basics (Problems 1–10)

Apply the 1% Method and multiplier technique wherever possible for faster solutions.
1

18% of a number is 72. Find the number.

6

By what percent is 240 greater than 200?

2

35% of a number exceeds 20% of the same number by 45. Find the number.

7

If A is 40% more than B, then B is what percent less than A?

3

A number is increased by 20% and becomes 360. Find the original number.

8

If A is 25% less than B, then B is what percent more than A?

4

A number is decreased by 25% and becomes 450. Find the original number.

9

A number is first increased by 10% and then by 20%. Find the net increase.

5

60% of a number equals 40% of another number. Find their ratio.

10

A value increases from 400 to 520. Find the percentage increase.

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Practice Set: Profit, Loss & Discount

Problems 11–20
11
A shopkeeper gives 20% discount on a product marked at 5000. Find SP.
12
A product is sold at 25% profit for 2500. Find CP.
13
A product is sold at 20% loss for 1600. Find CP.
14
Two successive discounts of 20% and 10% are offered. Find equivalent discount.
15
A shopkeeper marks goods 40% above CP and allows 20% discount. Find profit%.
16
Profit is 30% and SP exceeds CP by 900. Find CP.
17
An article sold for 1800 gives 20% profit. Find CP.
18
MP is 6000. After 20% discount, profit is 20%. Find CP.
19
Successive profits of 20% and 25%. Find net profit%.
20
Successive losses of 20% and 25%. Find net loss%.
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Practice Set: Population, Marks & Salary (Problems 21–30)

Population & Growth

1
Population increases by 20% from 5000. Find new population.
2
Population increases by 10% annually for 2 years. Find net increase%.
3
Population grows from 10000 to 12100 in 2 years. Find annual growth rate.
4
A town's population increases by 25% then decreases by 20%. Find net change.
5
Population of men and women are in ratio 3:2. Find percentage of women.

Examination & Marks

1
A student scores 360 marks out of 450. Find percentage.
2
Passing marks are 40%. A student gets 144 and fails by 36 marks. Find total marks.
3
A candidate scores 35% and fails by 30 marks. Another scores 45% and gets 10 marks more than pass marks. Find total marks.

Salary & Income

1
Salary increases by 20% from 25000. Find new salary.
2
Salary becomes 36000 after 20% increase. Find original salary.
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Advanced Mixed Problems — Bank Exam Focus (31–40)

⚠️

These are the most frequently repeated problem types in bank and competitive exams. Master these patterns first.

1
Income, Expenditure & Savings Monthly income Tk. 20,000, expenditure Tk. 16,000. Income increases by 25% and expenditure by 20%. Find the percentage increase in savings.
2
Price & Consumption (Constant Expenditure) Price rises by 20%. By what percent must consumption decrease to keep expenditure unchanged?
3
Mixture — Water Addition A vessel contains 100 litres of mixture with 20% water. How many litres of pure water must be added so that water becomes 40% of the new mixture?
4
Successive Salary Changes Salary increased by 10% then 20%. Find the total percentage increase.
5
Equal Increase & Decrease A number is increased by 50% and then decreased by 50%. Find the net effect.
6
Successive Discounts Successive discounts of 30% and 20%. Find the equivalent single discount.
7
More Than / Less Than A's income is 25% more than B's. By what percent is B's income less than A's?
8
Income Tax Reduction Income tax is reduced from 25% to 20%. Find the percentage reduction in tax.
9
Ratio to Percentage The ratio of A:B:C is 2:3:5. Find A as a percentage of the total.
10
Equal Profit & Loss Equal profit and loss of 20% on two articles sold at the same price. Find the net result.
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Advanced Mixed Problems — Extended Set (41–50)

20 more advanced mixed problems drawn from all categories — bank exam level difficulty.

11

Compound Population Growth

A city's population is 8,00,000. It grows at 5% per annum. Find the population after 2 years.

12

Depreciation

A machine costs ₹50,000 and depreciates at 10% per year. Find its value after 2 years.

13

Salary Cut & Restoration

A person's salary is cut by 20%. By what percent must it be raised to restore the original?

14

Expenditure Increase

A person's income increases by 10% but expenditure increases by 15%. Original savings = ₹5000. Find new savings.

15

Mixture — Milk & Water

A 60 litre mixture contains milk and water in ratio 4:1. How much water must be added to make ratio 4:2?

16

Discount Chain

Three successive discounts of 10%, 20%, and 25%. Find the equivalent single discount.

17

Marks Shortcut

A student scores 45% and fails by 15 marks. Passing % is 50%. Find total marks.

18

Two Students Comparison

A scores 30% and fails by 20 marks. B scores 40% and passes by 30 marks. Find total marks.

19

Tax & Net Income

Income tax rate increases from 10% to 15% on an income of ₹80,000. Find the increase in tax amount.

20

Investment Return

A sum invested at 25% profit gives ₹6250 profit. Find the original investment.

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Advanced Mixed Problems — Extended Set (51–60)

21
Price-Consumption
Price of petrol increases by 25%. By what % must a person reduce consumption to keep expenditure same?
22
Successive Profit
A trader buys at ₹800, marks up 50%, then gives 20% discount. Find profit%.
23
Population Decrease
A town's population was 1,25,000. It decreased by 4% in year 1 and increased by 5% in year 2. Find final population.
24
Salary Ratio
A's salary is 20% less than B's. B's salary is 25% more than C's. Find A's salary as % of C's.
25
Commission Problem
A salesman gets 5% commission on sales up to ₹10,000 and 7% on sales above that. He earns ₹950. Find his total sales.
26
Mixture Replacement
From 40 litres of pure milk, 8 litres is replaced with water. Again 8 litres is replaced. Find the % of milk now.
27
Exam Eligibility
In an exam, 60% students passed in English, 70% in Maths, and 40% in both. Find % failed in both.
28
Budget Allocation
A person spends 30% on rent, 25% on food, 15% on education. Remaining ₹6000 is savings. Find income.
29
Profit on Two Items
Two items sold at ₹4800 each. One at 20% profit, other at 20% loss. Find overall profit or loss.
30
Net Change Problem
The length of a rectangle is increased by 30% and breadth decreased by 20%. Find % change in area.
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Advanced: Percentage Basics — 20 Problems (61–80)

20 most important advanced-level Percentage Basics problems.

Focus on back-calculation, ratio, and multi-step percentage chains.

1
45% of a number is 315. Find 80% of that number.
2
A number is increased by 30%, then by 20%, then decreased by 25%. Find the net change.
3
Two numbers are in ratio 5:8. If the larger is 64, find 35% of the smaller.
4
15% of x = 20% of y. Find x:y.
5
A number when decreased by 40% gives 270. What is 60% of the original?
6
If 120% of A = 80% of B, find A:B.
7
A is 20% of B and B is 25% of C. What % is A of C?
8
The sum of 22% and 35% of a number is 399. Find the number.
9
A number is multiplied by 1.4 and then by 0.75. Find the net % change.
10
3/8 of a number is what % of 5/4 of the same number?
11
If x% of y = y% of z, find z in terms of x.
12
A value decreases by 12.5%. What multiplier was used?
13
60% of students are boys. 40% of boys play cricket. What % of all students play cricket?
14
A sum is divided among A, B, C in ratio 2:3:5. B's share is ₹4500. Find 25% of the total.
15
By what % is 5/4 greater than 4/5?
16
The difference between 38% and 22% of a number is 192. Find the number.
17
A candidate must score 45% to pass. He scores 288 and fails by 72. Find total marks.
18
If 35% of (A+B) = 45% of A, find A:B.
19
A value is first reduced to 80% and then to 75% of the result. Net % of original?
20
What % of 3 hours is 45 minutes?
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Advanced: Profit, Loss & Discount — 20 Problems (81–100)

20 most important advanced Profit, Loss & Discount problems.

Focus on marked price, successive discounts, and combined profit-loss chains.
1.
A dealer buys at ₹1200 and marks 50% above CP. What discount % must he give to sell at 20% profit?
2.
Selling price of 12 oranges equals CP of 15 oranges. Find profit%.
3.
A man sells two watches at ₹1980 each. One at 10% profit, another at 10% loss. Find net profit or loss amount.
4.
CP of 10 pens = SP of 8 pens. Find profit or loss%.
5.
A shopkeeper gives 3 articles free with every 12 purchased. Find effective discount%.
6.
MP is 40% above CP. Two successive discounts of 15% and 10% given. Find overall profit or loss%.
7.
A person sells at 12.5% loss. Had he sold for ₹360 more, he'd have gained 12.5%. Find CP.
8.
SP = ₹5040, discount = 10%, profit = 12%. Find MP and CP.
9.
Cost price ratio of A:B = 3:4. Profit ratio = 1:2. If total profit = ₹2100, find profit% on A.
10.
By selling 33 articles, a trader gains CP of 11 articles. Find profit%.
11.
Successive discounts of 25% and 20% on MP of ₹8000. Find SP.
12.
An article bought at ₹1500 and sold at 20% profit. If CP increases by 10%, what must SP be to maintain same profit%?
13.
A sells to B at 10% profit, B sells to C at 20% profit. C pays ₹2640. Find A's CP.
14.
Equivalent discount of two successive discounts equals 28%. One discount is 20%. Find the other.
15.
A shopkeeper allows 10% discount and still gains 26%. If CP = ₹700, find MP.
16.
Profit is 20% of SP. Find profit% on CP.
17.
A man buys 5 kg for ₹4 and sells 4 kg for ₹5. Find profit%.
18.
Loss% = Selling price in rupees. If CP = ₹400, find SP.
19.
A trader mixes two varieties costing ₹80 and ₹120 per kg in ratio 3:2 and sells at ₹132. Find profit%.
20.
SP of an article after 15% discount is ₹2550. Had no discount been given, profit would be 30%. Find CP.
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Advanced: Population, Marks & Salary — 20 Problems

20 most important advanced problems across Population, Marks & Salary categories.

These problem types appear in nearly every bank and competitive exam.

Section 1 — Population & Growth

1
Population of a city is 5,00,000. Grows at 4% in year 1 and 5% in year 2. Find population after 2 years.
2
A town's population was 2,56,000 two years ago. After growing at 25% each year, find current population.
3
Population decreases 10% in year 1 and increases 10% in year 2. Net % change?
4
Population of men to women is 7:5. Women are what % less than men?
5
A village population grows from 50,000 to 60,500 in 2 years. Find annual growth rate.
6
If population grows at 10% p.a., after how many years does it double? (approx)
7
A city's population increases by 20%, then decreases by 25%, then increases by 10%. Find net % change.

Section 2 — Examination & Marks

1
A student scores 480 out of 600. By what % did he exceed the passing marks of 40%?
2
A fails by 40 marks. B passes with 10% extra marks. A scored 40% and B scored 50%. Find total marks.
3
Three students score 60%, 70%, 80%. Average score is 630 marks. Find total marks of exam.
4
A student scores 35% and fails by 35 marks. Another scores 55% and exceeds pass mark by 45 marks. Find total marks.
5
Passing marks = 33%. A student gets 125 and fails by 40 marks. Find total marks.
6
In an exam, 40% failed in Hindi, 30% failed in English, 10% failed in both. Find % who passed in both.
7
A student gets 75% in 5 subjects with max 100 each. He got 90, 85, 70, 65 in 4 subjects. Find 5th subject marks.

Section 3 — Salary & Income

1
A's salary is 30% more than B's. B's salary is 20% less than C's. Find A's salary as % of C's.
2
Monthly income ₹50,000. Spends 60% on household, 20% on rent, 10% on education. Find monthly savings.
3
Salary increases 10% in year 1, 15% in year 2, decreases 20% in year 3 from original ₹40,000. Find final salary.
4
After 20% increment salary = ₹42,000. Find salary after another 15% increment on new salary.
5
A's income is ₹1,20,000 p.a. He pays 10% tax on first ₹60,000 and 20% tax on balance. Find net income.
6
Income cut by 25%, then raised by 25%. Net % change in income?
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Answer Key — All Practice Problems

Percentage Basics (1–10)

1. 400
2. 300
3. 300
4. 600
5. 2:3
6. 20%
7. 28.57%
8. 33.33%
9. 32%
10. 30%

Profit, Loss & Discount (11–20)

11. ₹4000
12. ₹2000
13. ₹2000
14. 28%
15. 12% profit
16. ₹3000
17. ₹1500
18. ₹4000
19. 50% profit
20. 40% loss

Population, Marks & Salary (21–30)

21. 6000
22. 21%
23. 10%
24. No change
25. 40%
26. 80%
27. 450
28. 400
29. ₹30000
30. ₹30000

Advanced Bank Exam (31–40)

31. 45% increase
32. 16⅔%
33. 33⅓ litres
34. 32%
35. 25% decrease
36. 44%
37. 20% less
38. 20% reduction
39. 20%
40. 4% net loss
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Answer Key — Extended & Category Sets

Advanced Mixed (41–50)

11.
8,82,000
12.
₹40,500
13.
25%
14.
₹500
15.
12 litres
16.
49.6%
17.
300
18.
400
19.
₹4000
20.
₹25,000

Advanced Mixed (51–60)

21.
20%
22.
20% profit
23.
1,26,000
24.
75%
25.
₹15,000
26.
64%
27.
10%
28.
₹20,000
29.
4% loss
30.
4% increase

Advanced Basics (61–80)

1.
504
2.
17.4% increase
3.
14
4.
4:3
5.
270
6.
2:3
7.
5%
8.
700
9.
5% increase
10.
60%
11.
z=x
12.
0.875
13.
24%
14.
₹3750
15.
56.25%
16.
1200
17.
720
18.
2:1
19.
60%
20.
25%

Advanced Profit/Loss (81–100)

1.
20%
2.
25%
3.
₹36 loss
4.
25% profit
5.
20%
6.
4.7% profit
7.
₹1440
8.
MP=₹5600, CP=₹4500
9.
25%
10.
33.33%
11.
₹4800
12.
₹1980
13.
₹2000
14.
10%
15.
₹980
16.
25%
17.
56.25%
18.
₹360
19.
20%
20.
₹2352

Population / Marks / Salary (Category Set)

POPULATION
5,46,000 / 4,00,000 / 1% decrease / 16.67% / 10% / ~7 yrs / 4.4% increase
MARKS
40% / 200 / 840 / 400 / 500 / 30% / 85
SALARY
104% / ₹5000 / ₹37,400 / ₹55,200 / ₹1,02,000 / 6.25% decrease
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Key Takeaways & Exam Strategy

Use the 1% Method First

Before any complex calculation, find 1% of the base value. It unlocks the entire problem instantly.

Memorize Net Change Formula

x + y + xy/100 solves most successive change problems in seconds. Use (−) for decreases.

Bank Exam Priority

Focus on: Income/Expenditure, Price-Consumption, Successive Discounts, and Equal Profit-Loss problems — these appear most often.

Always Verify with Multipliers

After solving, confirm using decimal multipliers: increase 20% = ×1.20, decrease 25% = ×0.75. Quick sanity check!

Master these 70 curated problems and all core shortcuts — you are well-prepared for any percentage question in bank and competitive exams.

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100 Advanced Percentage Problems for Bank & Govt Exams

Master percentage concepts with 100 practice problems, shortcuts, and formulas for bank and competitive exams. Includes profit, loss, and population growth.

100 Advanced Percentage Problems

A focused, exam-ready practice set for bank and competitive exams. Master core concepts, powerful shortcuts, and the most important problem types — all in one streamlined guide.

BANK EXAM PREP

CORE FORMULAS

SHORTCUTS

PRACTICE SET

Core Ideas of Percentages

Master these three foundational principles before solving any percentage problem.

The Concept of 100

A percentage is a fraction with 100 as its denominator. The Base Value (Original Number, Cost Price, Total Marks) is always 100%.

The 1% Method

Find 1% first, then scale up.

Decimal Multipliers

Core Formulas

Basic Calculations

% Value

(Percentage ÷ 100) × Total

20% of 150 = 30

% Share

(Part ÷ Whole) × 100

25 out of 200 = 12.5%

Original from %

(Given Value × 100) ÷ Given %

40 is 8% of what? = 500

Increase

[(New − Old) ÷ Old] × 100

60 to 75 = 25%

Decrease

[(Old − New) ÷ Old] × 100

80 to 68 = 15%

Original after increase

New ÷ (1 + r/100)

120 ÷ 1.2 = 100

Original after decrease

New ÷ (1 − r/100)

75 ÷ 0.75 = 100

Profit, Loss & Discount

Profit%

(Profit ÷ CP) × 100

Loss%

(Loss ÷ CP) × 100

SP after Discount

MP × (100 − Discount%) ÷ 100

Population Growth

After n years

P × (1 + r/100)ⁿ

n years ago

P ÷ (1 + r/100)ⁿ

Easy Shortcuts

Net Change (Successive Changes)

Two changes <span style='font-style: italic; color: #2563eb; font-weight: 600;'>x%</span> and <span style='font-style: italic; color: #2563eb; font-weight: 600;'>y%</span>:<br>Net = <strong style='color: #111827; font-size: 24px;'>x + y + <span style='font-size: 0.8em;'>(xy/100)</span></strong><br><br><span style='font-size: 18px; color: #6b7280;'>Use (+) for increase, (−) for decrease.</span>

<strong>Example:</strong> 10% increase then 5% decrease = 4.5% increase.

Equivalent Single Discount

Two discounts <span style='font-style: italic; color: #2563eb; font-weight: 600;'>d₁%</span> and <span style='font-style: italic; color: #2563eb; font-weight: 600;'>d₂%</span>:<br><div style='margin-top: 8px;'><strong style='color: #111827; font-size: 24px;'>d₁ + d₂ − <span style='font-size: 0.8em;'>(d₁×d₂)/100</span></strong></div>

<strong>Example:</strong> 20% and 10% → 28%.

More Than / Less Than

<span style='font-weight: 600;'>A is x% more than B</span><br>→ B is less than A by <strong style='color: #111827; font-size: 24px;'>x/(100+x) × 100</strong><div style='height: 16px;'></div><span style='font-weight: 600;'>A is x% less than B</span><br>→ B is more than A by <strong style='color: #111827; font-size: 24px;'>x/(100−x) × 100</strong>

<strong>Example:</strong> A is 25% more than B → B is 20% less than A.

Price & Consumption <span style='font-size: 16px; color: #6b7280; font-weight: 500; font-family: "Inter", sans-serif; display: block; margin-top: 4px;'>(Constant Expenditure)</span>

<span style='font-weight: 600;'>Price ↑ r%</span><br>→ Consumption ↓ by <strong style='color: #111827; font-size: 24px;'>r/(100+r) × 100</strong><div style='height: 16px;'></div><span style='font-weight: 600;'>Price ↓ r%</span><br>→ Consumption ↑ by <strong style='color: #111827; font-size: 24px;'>r/(100−r) × 100</strong>

<strong>Example:</strong> Price rises 20% → Consumption must fall 16.67%.

Equal Increase & Decrease

Increase by <span style='font-style: italic; color: #2563eb; font-weight: 600;'>x%</span> then decrease by <span style='font-style: italic; color: #2563eb; font-weight: 600;'>x%</span><br><div style='margin-top: 12px;'>→ Always net <strong>decrease</strong> of <strong style='color: #111827; font-size: 24px; background: #e5e7eb; padding: 4px 8px; border-radius: 4px;'>x²/100 %</strong></div>

<strong>Example:</strong> 10% up then 10% down = 1% net decrease.

Exam Marks Shortcut

<strong>Total Marks =</strong> <strong style='color: #111827; display: flex; align-items: center; margin-top: 12px; font-size: 18px; gap: 12px; background: #e5e7eb; padding: 12px 16px; border-radius: 8px; width: fit-content;'><div style='display: flex; flex-direction: column; align-items: center;'><span>(Failed by + Above pass)</span><span style='width: 100%; border-bottom: 2px solid #111827; margin: 4px 0;'></span><span>Difference in %</span></div><div>× 100</div></strong>

<strong>Example:</strong> fails by 12, above pass 18, differ 6% → total = 500.

Practice Set: Percentage Basics (Problems 1–10)

Apply the 1% Method and multiplier technique wherever possible for faster solutions.

18% of a number is 72. Find the number.

35% of a number exceeds 20% of the same number by 45. Find the number.

A number is increased by 20% and becomes 360. Find the original number.

A number is decreased by 25% and becomes 450. Find the original number.

60% of a number equals 40% of another number. Find their ratio.

By what percent is 240 greater than 200?

If A is 40% more than B, then B is what percent less than A?

If A is 25% less than B, then B is what percent more than A?

A number is first increased by 10% and then by 20%. Find the net increase.

A value increases from 400 to 520. Find the percentage increase.

Practice Set: Profit, Loss & Discount

Problems 11–20

A shopkeeper gives 20% discount on a product marked at 5000. Find SP.

A product is sold at 25% profit for 2500. Find CP.

A product is sold at 20% loss for 1600. Find CP.

Two successive discounts of 20% and 10% are offered. Find equivalent discount.

A shopkeeper marks goods 40% above CP and allows 20% discount. Find profit%.

Profit is 30% and SP exceeds CP by 900. Find CP.

An article sold for 1800 gives 20% profit. Find CP.

MP is 6000. After 20% discount, profit is 20%. Find CP.

Successive profits of 20% and 25%. Find net profit%.

Successive losses of 20% and 25%. Find net loss%.

Practice Set: Population, Marks & Salary (Problems 21–30)

Population & Growth

Population increases by 20% from 5000. Find new population.

Population increases by 10% annually for 2 years. Find net increase%.

Population grows from 10000 to 12100 in 2 years. Find annual growth rate.

A town's population increases by 25% then decreases by 20%. Find net change.

Population of men and women are in ratio 3:2. Find percentage of women.

Examination & Marks

A student scores 360 marks out of 450. Find percentage.

Passing marks are 40%. A student gets 144 and fails by 36 marks. Find total marks.

A candidate scores 35% and fails by 30 marks. Another scores 45% and gets 10 marks more than pass marks. Find total marks.

Salary & Income

Salary increases by 20% from 25000. Find new salary.

Salary becomes 36000 after 20% increase. Find original salary.

Advanced Mixed Problems — Bank Exam Focus (31–40)

These are the most frequently repeated problem types in bank and competitive exams. Master these patterns first.

1

Income, Expenditure & Savings

Monthly income Tk. 20,000, expenditure Tk. 16,000. Income increases by 25% and expenditure by 20%. Find the percentage increase in savings.

2

Price & Consumption (Constant Expenditure)

Price rises by 20%. By what percent must consumption decrease to keep expenditure unchanged?

3

Mixture — Water Addition

A vessel contains 100 litres of mixture with 20% water. How many litres of pure water must be added so that water becomes 40% of the new mixture?

4

Successive Salary Changes

Salary increased by 10% then 20%. Find the total percentage increase.

5

Equal Increase & Decrease

A number is increased by 50% and then decreased by 50%. Find the net effect.

6

Successive Discounts

Successive discounts of 30% and 20%. Find the equivalent single discount.

7

More Than / Less Than

A's income is 25% more than B's. By what percent is B's income less than A's?

8

Income Tax Reduction

Income tax is reduced from 25% to 20%. Find the percentage reduction in tax.

9

Ratio to Percentage

The ratio of A:B:C is 2:3:5. Find A as a percentage of the total.

10

Equal Profit & Loss

Equal profit and loss of 20% on two articles sold at the same price. Find the net result.

Advanced Mixed Problems — Extended Set (41–50)

20 more advanced mixed problems drawn from all categories — bank exam level difficulty.

Compound Population Growth

A city's population is 8,00,000. It grows at 5% per annum. Find the population after 2 years.

Depreciation

A machine costs ₹50,000 and depreciates at 10% per year. Find its value after 2 years.

Salary Cut & Restoration

A person's salary is cut by 20%. By what percent must it be raised to restore the original?

Expenditure Increase

A person's income increases by 10% but expenditure increases by 15%. Original savings = ₹5000. Find new savings.

Mixture — Milk & Water

A 60 litre mixture contains milk and water in ratio 4:1. How much water must be added to make ratio 4:2?

Discount Chain

Three successive discounts of 10%, 20%, and 25%. Find the equivalent single discount.

Marks Shortcut

A student scores 45% and fails by 15 marks. Passing % is 50%. Find total marks.

Two Students Comparison

A scores 30% and fails by 20 marks. B scores 40% and passes by 30 marks. Find total marks.

Tax & Net Income

Income tax rate increases from 10% to 15% on an income of ₹80,000. Find the increase in tax amount.

Investment Return

A sum invested at 25% profit gives ₹6250 profit. Find the original investment.

Advanced Mixed Problems — Extended Set (51–60)

Price-Consumption

Price of petrol increases by 25%. By what % must a person reduce consumption to keep expenditure same?

Successive Profit

A trader buys at ₹800, marks up 50%, then gives 20% discount. Find profit%.

Population Decrease

A town's population was 1,25,000. It decreased by 4% in year 1 and increased by 5% in year 2. Find final population.

Salary Ratio

A's salary is 20% less than B's. B's salary is 25% more than C's. Find A's salary as % of C's.

Commission Problem

A salesman gets 5% commission on sales up to ₹10,000 and 7% on sales above that. He earns ₹950. Find his total sales.

Mixture Replacement

From 40 litres of pure milk, 8 litres is replaced with water. Again 8 litres is replaced. Find the % of milk now.

Exam Eligibility

In an exam, 60% students passed in English, 70% in Maths, and 40% in both. Find % failed in both.

Budget Allocation

A person spends 30% on rent, 25% on food, 15% on education. Remaining ₹6000 is savings. Find income.

Profit on Two Items

Two items sold at ₹4800 each. One at 20% profit, other at 20% loss. Find overall profit or loss.

Net Change Problem

The length of a rectangle is increased by 30% and breadth decreased by 20%. Find % change in area.

Advanced: Percentage Basics — 20 Problems (61–80)

20 most important advanced-level Percentage Basics problems.

Focus on back-calculation, ratio, and multi-step percentage chains.

45% of a number is 315. Find 80% of that number.

A number is increased by 30%, then by 20%, then decreased by 25%. Find the net change.

Two numbers are in ratio 5:8. If the larger is 64, find 35% of the smaller.

15% of x = 20% of y. Find x:y.

A number when decreased by 40% gives 270. What is 60% of the original?

If 120% of A = 80% of B, find A:B.

A is 20% of B and B is 25% of C. What % is A of C?

The sum of 22% and 35% of a number is 399. Find the number.

A number is multiplied by 1.4 and then by 0.75. Find the net % change.

3/8 of a number is what % of 5/4 of the same number?

If x% of y = y% of z, find z in terms of x.

A value decreases by 12.5%. What multiplier was used?

60% of students are boys. 40% of boys play cricket. What % of all students play cricket?

A sum is divided among A, B, C in ratio 2:3:5. B's share is ₹4500. Find 25% of the total.

By what % is 5/4 greater than 4/5?

The difference between 38% and 22% of a number is 192. Find the number.

A candidate must score 45% to pass. He scores 288 and fails by 72. Find total marks.

If 35% of (A+B) = 45% of A, find A:B.

A value is first reduced to 80% and then to 75% of the result. Net % of original?

What % of 3 hours is 45 minutes?

Advanced: Profit, Loss & Discount — 20 Problems (81–100)

20 most important advanced Profit, Loss & Discount problems.

Focus on marked price, successive discounts, and combined profit-loss chains.

A dealer buys at ₹1200 and marks 50% above CP. What discount % must he give to sell at 20% profit?

Selling price of 12 oranges equals CP of 15 oranges. Find profit%.

A man sells two watches at ₹1980 each. One at 10% profit, another at 10% loss. Find net profit or loss amount.

CP of 10 pens = SP of 8 pens. Find profit or loss%.

A shopkeeper gives 3 articles free with every 12 purchased. Find effective discount%.

MP is 40% above CP. Two successive discounts of 15% and 10% given. Find overall profit or loss%.

A person sells at 12.5% loss. Had he sold for ₹360 more, he'd have gained 12.5%. Find CP.

SP = ₹5040, discount = 10%, profit = 12%. Find MP and CP.

Cost price ratio of A:B = 3:4. Profit ratio = 1:2. If total profit = ₹2100, find profit% on A.

By selling 33 articles, a trader gains CP of 11 articles. Find profit%.

Successive discounts of 25% and 20% on MP of ₹8000. Find SP.

An article bought at ₹1500 and sold at 20% profit. If CP increases by 10%, what must SP be to maintain same profit%?

A sells to B at 10% profit, B sells to C at 20% profit. C pays ₹2640. Find A's CP.

Equivalent discount of two successive discounts equals 28%. One discount is 20%. Find the other.

A shopkeeper allows 10% discount and still gains 26%. If CP = ₹700, find MP.

Profit is 20% of SP. Find profit% on CP.

A man buys 5 kg for ₹4 and sells 4 kg for ₹5. Find profit%.

Loss% = Selling price in rupees. If CP = ₹400, find SP.

A trader mixes two varieties costing ₹80 and ₹120 per kg in ratio 3:2 and sells at ₹132. Find profit%.

SP of an article after 15% discount is ₹2550. Had no discount been given, profit would be 30%. Find CP.

Advanced: Population, Marks & Salary — 20 Problems

20 most important advanced problems across Population, Marks & Salary categories.

These problem types appear in nearly every bank and competitive exam.

Section 1 — Population & Growth

Population of a city is 5,00,000. Grows at 4% in year 1 and 5% in year 2. Find population after 2 years.

A town's population was 2,56,000 two years ago. After growing at 25% each year, find current population.

Population decreases 10% in year 1 and increases 10% in year 2. Net % change?

Population of men to women is 7:5. Women are what % less than men?

A village population grows from 50,000 to 60,500 in 2 years. Find annual growth rate.

If population grows at 10% p.a., after how many years does it double? (approx)

A city's population increases by 20%, then decreases by 25%, then increases by 10%. Find net % change.

Section 2 — Examination & Marks

A student scores 480 out of 600. By what % did he exceed the passing marks of 40%?

A fails by 40 marks. B passes with 10% extra marks. A scored 40% and B scored 50%. Find total marks.

Three students score 60%, 70%, 80%. Average score is 630 marks. Find total marks of exam.

A student scores 35% and fails by 35 marks. Another scores 55% and exceeds pass mark by 45 marks. Find total marks.

Passing marks = 33%. A student gets 125 and fails by 40 marks. Find total marks.

In an exam, 40% failed in Hindi, 30% failed in English, 10% failed in both. Find % who passed in both.

A student gets 75% in 5 subjects with max 100 each. He got 90, 85, 70, 65 in 4 subjects. Find 5th subject marks.

Section 3 — Salary & Income

A's salary is 30% more than B's. B's salary is 20% less than C's. Find A's salary as % of C's.

Monthly income ₹50,000. Spends 60% on household, 20% on rent, 10% on education. Find monthly savings.

Salary increases 10% in year 1, 15% in year 2, decreases 20% in year 3 from original ₹40,000. Find final salary.

After 20% increment salary = ₹42,000. Find salary after another 15% increment on new salary.

A's income is ₹1,20,000 p.a. He pays 10% tax on first ₹60,000 and 20% tax on balance. Find net income.

Income cut by 25%, then raised by 25%. Net % change in income?

Answer Key — All Practice Problems

Percentage Basics (1–10)

Profit, Loss & Discount (11–20)

Population, Marks & Salary (21–30)

Advanced Bank Exam (31–40)

400

300

300

600

2:3

20%

28.57%

33.33%

32%

30%

₹4000

₹2000

₹2000

28%

12% profit

₹3000

₹1500

₹4000

50% profit

40% loss

6000

21%

10%

No change

40%

80%

450

400

₹30000

₹30000

45% increase

16⅔%

33⅓ litres

32%

25% decrease

44%

20% less

20% reduction

20%

4% net loss

Answer Key — Extended & Category Sets

Advanced Mixed (41–50)

Advanced Mixed (51–60)

Advanced Basics (61–80)

Advanced Profit/Loss (81–100)

Population / Marks / Salary (Category Set)

Key Takeaways & Exam Strategy

Use the 1% Method First

Before any complex calculation, find 1% of the base value. It unlocks the entire problem instantly.

Memorize Net Change Formula

<span style="font-family: 'Courier New', Courier, monospace; font-weight: 700; background: #e0e7ff; padding: 2px 8px; border-radius: 4px; color: #1a237e;">x + y + xy/100</span> solves most successive change problems in seconds. Use <strong style="color:#1e3a8a;">(−)</strong> for decreases.

Bank Exam Priority

Focus on: <strong style="color:#1e3a8a;">Income/Expenditure</strong>, <strong style="color:#1e3a8a;">Price-Consumption</strong>, <strong style="color:#1e3a8a;">Successive Discounts</strong>, and <strong style="color:#1e3a8a;">Equal Profit-Loss</strong> problems — these appear most often.

Always Verify with Multipliers

After solving, confirm using decimal multipliers: increase 20% = <strong style="color:#1e3a8a;">×1.20</strong>, decrease 25% = <strong style="color:#1e3a8a;">×0.75</strong>. Quick sanity check!

Master these 70 curated problems and all core shortcuts — you are well-prepared for any percentage question in bank and competitive exams.