Percentage for IBPS PO

Percentage is rarely asked on its own for long, but it hides inside almost everything else. Profit and loss is percentage on cost price. Interest is percentage over time. Every DI set asks for growth, share or "what per cent of". If percentage is slow or shaky, the whole quant section is slow and shaky.

The good news is that the topic rests on one idea, the base, and a handful of patterns built on it. Learn those patterns with the reason behind each, and a large share of the paper gets faster.

The one rule: know your base

A percentage is always a percentage of something. That something is the base, and it goes in the denominator.

• "A is 25% more than B": the base is B. A = 1.25B.
• "Percentage change from 2024 to 2025": the base is 2024.
• "B is what percentage less than A": the base is A.

Nearly every percentage mistake is a wrong base.

Fraction equivalents to know by heart

Why they matter: 16.67% of 474 is slow, but 474 ÷ 6 = 79 is quick. Converting to a fraction turns a multiplication into a single division.

The core methods

1. Multiplying factors. An increase of r% multiplies by (1 + r/100). A decrease of r% multiplies by (1 − r/100). A 20% rise is × 1.2; a 15% fall is × 0.85.

2. Reverse percentage. If a value after an r% increase is V, the original is V ÷ (1 + r/100). Why: the change was a multiplication, so undo it by dividing. Never subtract r% of V from V; that uses the new value as the base.

3. Successive changes. Changes of a% and then b% give a net change of a + b + ab/100 per cent. Use negative signs for decreases. Why: (1 + a/100)(1 + b/100) = 1 + (a + b)/100 + ab/10,000. The last term, written as a percentage, is ab/100.

4. More than and less than. If A is r% more than B, then B is r ÷ (100 + r) × 100 per cent less than A. Why: the difference is r units, but the base changes from 100 (B) to 100 + r (A).

5. Price, consumption and expenditure. Expenditure = price × consumption. If price rises by r%, consumption must fall by r ÷ (100 + r) × 100 per cent to keep expenditure unchanged. This is method 4 again.

Eight worked examples

Example 1: A's income is 25% more than B's. By what percentage is B's income less than A's?

• 25 ÷ 125 × 100 = 20%.
• Check with numbers: B = 100, A = 125. The difference is 25, which is 20% of 125.

Example 2: A number is increased by 20% and then decreased by 20%. The result is 480. Find the original number.

• Net factor = 1.2 × 0.8 = 0.96.
• Original = 480 ÷ 0.96 = 500.

Example 3: In an election between two candidates, 10% of the votes cast were invalid. The winner got 55% of the valid votes and won by 1,800 votes. How many votes were cast?

• Margin = 55% − 45% = 10% of valid votes = 1,800. Valid votes = 18,000.
• Valid votes are 90% of the total. Total = 18,000 ÷ 0.9 = 20,000.

Example 4: The price of sugar rises by 25%. By what percentage must a family reduce consumption to keep expenditure the same?

• 25 ÷ 125 × 100 = 20%.
• Check: 1.25 × 0.8 = 1.

Example 5: A town of 20,000 grows by 10% in one year and falls by 10% the next. What is the population after two years?

• 20,000 × 1.1 × 0.9 = 19,800.
• By the successive-change rule: 10 − 10 − 100/100 = −1%. A 10% rise followed by a 10% fall is always a 1% net fall.

Example 6: A student needs 40% to pass. They score 180 marks and fail by 20 marks. What are the maximum marks?

• Pass mark = 180 + 20 = 200 = 40% of the maximum.
• Maximum = 200 ÷ 0.4 = 500.

Example 7: An aspirant spends 75% of their income. Income rises by 20% and expenditure by 10%. By what percentage do savings rise?

• Take income as 100. Expenditure 75, savings 25.
• New income 120, new expenditure 82.5, new savings 37.5.
• Rise = 12.5 ÷ 25 × 100 = 50%.

Example 8: 40% of A equals 60% of B. Find A : B.

• 0.4A = 0.6B, so A/B = 0.6/0.4 = 3 : 2.

Common mistakes

• Using the final value as the base in reverse questions.
• Adding successive changes. A 10% rise and a 20% rise make 32%, not 30%.
• Forgetting invalid votes in election questions. The candidates' percentages are usually of valid votes.
• Mixing up percentage points and per cent in DI answers.
• Assuming savings change by the same percentage as income. Work through income and expenditure with 100 as the base.

Practice set

1. The price of an item rises by 20%. By what percentage must consumption fall to keep spending the same?
2. In a two-candidate election with no invalid votes, the winner gets 55% of the votes and wins by 1,500 votes. Find the total votes.
3. A salary is raised by 10% and then by 20%. What is the total percentage increase?
4. 30% of a number is 20 less than 40% of the same number. Find the number.
5. After a 12.5% fall, the price of an item is ₹1,400. What was the original price?
6. A's salary is 20% less than B's. By what percentage is B's salary more than A's?
7. A person saves 20% of their income. Income rises by 25% and expenditure by 20%. By what percentage do savings rise?
8. A number is increased by 30% and then decreased by 30%. What is the net percentage change?

Answers:

1. 16⅔%. 20 ÷ 120 × 100.
2. 15,000. The margin is 10% of the votes, so 10% = 1,500.
3. 32%. 10 + 20 + (10 × 20)/100.
4. 200. The gap is 10% of the number, so 10% = 20.
5. ₹1,600. 1,400 ÷ 0.875.
6. 25%. Take B = 100, A = 80. The difference 20 is 25% of 80.
7. 45%. Income 100 to 125, expenditure 80 to 96, savings 20 to 29. 9 ÷ 20 × 100 = 45.
8. A 9% fall. 30 − 30 − (30 × 30)/100 = −9. Check: 1.3 × 0.7 = 0.91.

What to do next

• Memorise the fraction table until 1/7, 1/9, 1/11 and 1/12 are instant.
• Solve 15 mixed percentage questions a day for a week, writing the base for each before calculating.
• Apply the same methods in profit, loss and discount and table DI.
• Use the quant plan to fit percentage into your weekly schedule.