Percentage for IBPS Clerk

Percentage means "per hundred". It is rarely the most visible topic in the clerk numerical section, but it is inside almost everything else: every DI set, most approximation questions, profit and loss, interest and ratio word problems. A candidate who is slow at percentages is slow across the whole section.

The good news is that percentage questions follow a small number of patterns. Learn each one with the reason behind it and you can solve most in under 40 seconds.

Fractions to know cold

These pairs turn a percentage into a single division. 37.5% of 640 is 3/8 of 640: 640 ÷ 8 = 80, then 80 × 3 = 240.

The methods, and why they work

x% of y = y% of x

16% of 25 is the same as 25% of 16, which is 4. Both equal x × y ÷ 100, so you can swap them whenever one side is easier.

Percentage change

Percentage change = (new − old) ÷ old × 100. The base is the original value because the question asks how much the value changed relative to where it started.

Successive changes

A change of a% followed by b% gives a net change of a + b + ab/100. Use negative signs for decreases.

Why: the value becomes (1 + a/100)(1 + b/100) times the original. Expanding gives 1 + a/100 + b/100 + ab/10,000, which is a net change of a + b + ab/100 per cent. The ab/100 term is the "change on the change".

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: take B = 100, so A = 100 + r. The difference is r, but the question now measures it against A, so the base is 100 + r. The mirror rule: if A is r% less than B, then B is r ÷ (100 − r) × 100 per cent more than A.

Reverse percentage

If a value after an r% increase is V, the original is V ÷ (1 + r/100). You divide, because the increase was a multiplication.

Consumption and expenditure

If the price rises by r% and spending must stay the same, consumption must fall by r ÷ (100 + r) × 100 per cent. This is the same "more than, less than" rule: spending = price × quantity, so if price is (100 + r)/100 times, quantity must be 100/(100 + r) times.

Worked examples

Example 1. Find 36% of 75.

1. Swap: 36% of 75 = 75% of 36.
2. 75% is 3/4, and 3/4 of 36 = 27.

Example 2. A price rises by 20% and then falls by 10%. What is the net change?

1. a = 20, b = −10. Net = 20 − 10 + (20 × −10)/100 = 10 − 2 = 8.
2. 8% increase. Check with 100: 100 → 120 → 108.

Example 3. A's salary is 20% more than B's. By what percentage is B's salary less than A's?

1. 20 ÷ 120 × 100 = 1/6 × 100.
2. 16.67%. Check: B = 100, A = 120; the gap of 20 is 1/6 of 120.

Example 4. After a 15% increase, the price of a book is ₹920. What was the original price?

1. Original × 1.15 = 920.
2. Original = 920 ÷ 1.15 = ₹800. Check: 15% of 800 is 120, and 800 + 120 = 920.

Example 5. The price of sugar rises by 25%. By how much must a family cut consumption to keep spending the same?

1. 25 ÷ 125 × 100 = 1/5 × 100.
2. 20%. Check: price 100 → 125; quantity 100 → 80; spending 100 × 100 = 125 × 80 = 10,000.

Example 6. A candidate scores 35% and fails by 24 marks. The pass mark is 41%. What are the maximum marks?

1. The gap between 35% and 41% is 6%, and it equals 24 marks.
2. 1% = 4 marks, so the maximum is 400. Check: pass mark 164, the candidate scored 140, gap 24.

Percent and percentage points

If an interest rate rises from 8% to 10%, it rose by 2 percentage points but by 25 per cent (2 ÷ 8 × 100). DI questions and options use both, so read which one is asked.

Common mistakes

• Taking percentage change on the new value instead of the old.
• Adding successive percentages directly: +20% then +10% is 32%, not 30%.
• Assuming a rise of 25% and a fall of 25% cancel out. They give a net loss of 6.25%.
• Multiplying instead of dividing in reverse percentage: the original price before a 15% rise is not 85% of the new price.
• Confusing percentage points with per cent.

Practice

Set a 5-minute timer.

1. 12% of 50 = ?
2. A price rises by 30% and then falls by 20%. Net change?
3. A is 40% more than B. By what percentage is B less than A?
4. After a 20% decrease, a price is ₹640. What was the original price?
5. Petrol becomes 20% dearer. By how much must consumption fall to keep spending the same?
6. A candidate scoring 30% fails by 30 marks; another scoring 45% gets 15 marks more than the pass mark. Find the maximum marks.
7. A town of 40,000 grows by 5% a year. What is its population after 2 years?
8. A rate rises from 8% to 10%. What is the rise in percentage points, and in per cent?

Answers:

1. 6. Swap to 50% of 12.
2. 4% increase. 30 − 20 − 6 = 4. Check: 100 → 130 → 104.
3. 28.57%. 40 ÷ 140 × 100 = 2/7 × 100.
4. ₹800. 640 ÷ 0.8.
5. 16.67%. 20 ÷ 120 × 100 = 1/6 × 100.
6. 300. The gap is 45% − 30% = 15%, which equals 30 + 15 = 45 marks. So 1% = 3 marks. Pass mark 120 (40%).
7. 44,100. 40,000 × 1.05 = 42,000; 42,000 × 1.05 = 44,100.
8. 2 percentage points; 25%. 2 ÷ 8 × 100.

What to do next

• Memorise the fraction table and test yourself on it each morning for a week.
• Solve ten mixed percentage questions a day with the base table beside you, then without it.
• Apply the same rules in profit, loss and discount and in data interpretation.
• Revisit approximation, where most questions hide a percentage.