Percentage Tricks for SSC, RRB and IBPS: The Fraction Method That Saves Minutes

You know the feeling. The question says "a number is increased by 20% and then decreased by 20%", you start writing 100, then 120, then 96, and by the time you have circled the option you have spent a minute on something the paper expected in fifteen seconds. Multiply that by five or six percentage-flavoured questions in a section and it is the difference between finishing the quant section and leaving the last four unattempted.

Percentage is the one chapter where speed is almost entirely a matter of memory, not intelligence. Nobody is born able to see that 37.5% of 1,280 is 480. They just remember that 37.5% is 3/8. This post is about building that memory in a sensible order, and about the handful of shortcuts that turn most percentage questions into one-line arithmetic. Every example below has been worked through and checked, so you can copy the method without worrying that a stray number is wrong.

Percentage is also not a stand-alone chapter. It sits underneath profit and loss, simple and compound interest, data interpretation, mixtures, ratio and partnership. If your percentage is weak, everything in the maths section feels slower than it should. If it is strong, half of those chapters get easier for free. That is why it deserves a full week of your time early in the plan, before you touch anything fancier.

The exact number of questions and the marking scheme change with each notification, so check the latest one for your exam. What does not change is that percentage-based arithmetic shows up across SSC, RRB and bank papers in one form or another.

Start with the fraction table, not with formulas

Percent means "per hundred", and 25% means 25/100, which is 1/4. Most of the tricks in this chapter are just that idea used repeatedly. If you convert the percentage to its fraction, you can usually divide instead of multiply, and division by 2, 3, 4, 5 or 8 is something your head does faster than multiplying by 37.5.

Learn this table until you can recite it without looking. Write it on a sheet, stick it above your desk, and read it every day for a week. It is the most valuable single page in quant.

Fraction	Percentage	Fraction	Percentage
1/2	50%	1/9	11.11%
1/3	33.33%	1/10	10%
1/4	25%	1/11	9.09%
1/5	20%	1/12	8.33%
1/6	16.67%	1/13	7.69%
1/7	14.28%	1/14	7.14%
1/8	12.5%	1/15	6.67%
		1/16	6.25%

Two extensions matter just as much. Once you know 1/8 = 12.5%, you also know 3/8 = 37.5%, 5/8 = 62.5% and 7/8 = 87.5%. Once you know 1/6 = 16.67%, you know 5/6 = 83.33%. You do not memorise 30 numbers; you memorise a dozen and multiply.

Now use it. What is 16.67% of 462? It is 1/6 of 462, and 462 divided by 6 is 77. What is 12.5% of 640? One-eighth of 640 is 80. What is 37.5% of 1,280? Three-eighths, so 1,280 / 8 = 160, times 3 = 480. What is 8.33% of 2,400? One-twelfth, which is 200. Nothing in those steps needed a pen.

The habit to build: the moment you see a percentage, ask which fraction it is. If it is not one of the table entries, it is usually a multiple of one (like 37.5%, 62.5%, 83.33%) or it is a plain number you can compute as 1% and scale (like 17% or 23%).

Fractions from the other side

The table also works backwards, and this is where a lot of students lose time. If a question says "45 is what percent of 60?", do not compute 45 x 100 / 60. Simplify 45/60 to 3/4 and read off 75%. If it says "what percent of 75 is 12?", the fraction 12/75 is 4/25, and since 4/25 = 16/100, the answer is 16%. That last one needs a small step, but it is still quicker than long division, because you scale the denominator to 100 and read the numerator.

When the fraction is not clean, estimate against the table first. Is 17 out of 90 more or less than 1/5? Since 1/5 of 90 is 18, it is slightly under 20%. If the options are 15%, 18.9%, 22% and 25%, you are done: the answer is 18.9%.

Percentage of a number is symmetric

This one is small but saves real time in mental calculation: x% of y equals y% of x. So 18% of 50 is the same as 50% of 18, which is 9. And 4% of 75 is 75% of 4, which is 3. Whenever the percentage is awkward and the number is friendly, flip them.

Try it on a typical grumbling question: "What is 6% of 250?" Flip it: 250% of 6 is 15. Or "what is 12% of 25?" That is 25% of 12, which is 3. It looks like a party trick until you use it thirty times in a mock.

Successive changes: the a + b + ab/100 rule

This is the single most useful formula in the chapter. If a quantity changes by a% and then by b%, the net change is

a + b + (ab/100) percent

with a positive number for an increase and a negative one for a decrease. That is all. The formula is just (1 + a/100)(1 + b/100) minus 1, expanded, but you only need the shortcut.

Take the opening example: +20% then -20%. The net change is 20 - 20 + (20 x -20)/100 = -4%. So the number ends up 4% lower, not unchanged. That is the mistake in many wrong answers: students assume a rise and a fall of the same size cancel out. They never do, because the second percentage is applied to a different base.

More examples that come up constantly:

• Price rises 25% and then 20%. Net = 25 + 20 + (25 x 20)/100 = 45 + 5 = 50%. Check by multiplication: 1.25 x 1.2 = 1.5. Correct.
• A price falls 10% and then rises 30%. Net = -10 + 30 + (-10 x 30)/100 = 20 - 3 = 17% increase. Check: 0.9 x 1.3 = 1.17. Correct.
• The population of a town is 40,000. It grows 10% in the first year and 20% in the second. The final figure is 40,000 x 1.1 x 1.2 = 52,800. Net change is 10 + 20 + 2 = 32%, and 32% of 40,000 is 12,800, so 40,000 + 12,800 = 52,800. Both routes agree.
• A town has 50,000 people. It grows 8% in one year and then shrinks 10% the next. The result is 50,000 x 1.08 x 0.9 = 48,600. Net change = 8 - 10 - 0.8 = -2.8%, and 2.8% of 50,000 is 1,400, so 50,000 - 1,400 = 48,600. Same.

The rule chains. For three changes, apply it to the first two, then apply it again to that result and the third. In the exam you rarely need more than two.

The special case: same percentage twice

If the same percentage x is applied in the same direction twice, the net change is 2x + x^2/100. So a 10% rise twice is 20 + 1 = 21%. A side increased by 10% makes the area 21% larger (because area is side squared). A radius increased by 20% makes the area larger by 40 + 4 = 44%. Check: 1.2 x 1.2 = 1.44. Yes.

Area questions are the most common disguised use of this rule. If the length rises by 20% and the breadth falls by 10%, the area changes by 20 - 10 - 2 = 8%, and 1.2 x 0.9 = 1.08 confirms it. Do not compute new length and new breadth separately; you are wasting time.

Increase and decrease: reverse percentages

A very common structure: "the price of an item goes up by 25%. By what percent should consumption be reduced so that expenditure stays the same?" Students freeze because there are two unknowns, but the trick is a single fraction.

Convert the change to a fraction. 25% up is 1/4, so the new price is 5/4 of the old price. To keep spending unchanged, consumption must become 4/5 of the old. That is a drop of 1/5, which is 20%. So the rule in words: if something goes up by 1/n, the reverse drop is 1/(n+1). If something goes down by 1/n, the reverse rise is 1/(n-1).

Some pairs you should simply remember:

If price rises by	Consumption must fall by
10% (1/10)	9.09% (1/11)
20% (1/5)	16.67% (1/6)
25% (1/4)	20% (1/5)
33.33% (1/3)	25% (1/4)
50% (1/2)	33.33% (1/3)
100%	50%

Read the table the other way for a price fall: if price falls 20%, consumption can rise by 25%. If price falls 25%, consumption can rise 33.33%.

The same idea handles the classic "A's salary is 25% more than B's. By what percent is B's salary less than A's?" A is 5/4 of B, so B is 4/5 of A, which is 1/5 less, so 20%. If instead the question says "B's salary is 20% less than A's, so how much more is A's than B's?", A is 5/4 of B, 25% more. The base changes, so the answer changes. Always ask what the percentage is "of".

Base shifting with ratios

Ratio-based percentage questions are easy once you stop converting ratios to numbers.

If A : B = 3 : 5, then A is 3/5 of B, which is 60%. B is 5/3 of A, which is 166.67% of A, so B is 66.67% more than A. You can read any of these off directly. The mistake here is to compute A as a percentage of the total (3/8 = 37.5%) when the question asks about B, or vice versa. Read the question twice for the word "of".

Another form: "The ratio of two numbers is 4 : 5. What percent is the smaller of the larger?" 4/5 = 80%. And the larger is 25% more than the smaller (5/4 = 1.25). Both come from the same fraction; only the base differs. A simple check: whenever you get "x% more than", the base is the smaller quantity, and whenever you get "x% less than", the base is the larger one. If your answer for "more than" is bigger than 100% when the two quantities are close, something is off.

Election and vote questions

These are pure percentage with a few layers. The pattern is: total voters, some percentage did not vote, some percentage of votes were invalid, the winner got some percentage of the valid votes, find the margin or the number of votes.

Here is one worked through. In an election, 20,000 people were on the electoral roll and 80% voted. Of those who voted, 5% of the votes were invalid. The winning candidate got 60% of the valid votes and the only other candidate got the rest. What was the winning margin?

• Votes cast: 80% of 20,000 = 16,000.
• Valid votes: 95% of 16,000 = 15,200.
• Winner: 60% of 15,200 = 9,120. Loser: 6,080.
• Margin: 9,120 - 6,080 = 3,040.

There is a shortcut for the margin: it is (60 - 40)% = 20% of the valid votes, and 20% of 15,200 is 3,040. In a two-candidate contest, the margin is always the difference of their percentages times the valid votes. That skips two steps.

Do not multiply everything as decimals. Chain the fractions: 4/5 of 20,000 = 16,000, then 19/20 of 16,000 = 15,200. Or write 0.8 x 0.95 x 20,000 x 0.2, which is one expression. Either works, but do not calculate each stage on paper and re-type the numbers.

Marks, pass and fail

A classic: a student needs 40% to pass, scores 180 marks and fails by 20 marks. What are the total marks?

Pass mark is 180 + 20 = 200, and that is 40% of the total. So the total is 200 / 0.4 = 500. In fraction terms, 40% is 2/5, so 200 is 2/5 of the total and the total is 200 x 5/2 = 500.

The variants: "he fails by 20 marks if he gets 180" and "another student gets 240 and passes by 40", where you set up two lines and subtract. Always turn the sentences into pass mark = something, and use that.

A related structure is the inclusion-exclusion type: in an exam, 30% failed in maths, 25% failed in English and 10% failed in both. What percent passed in both? Failed in at least one = 30 + 25 - 10 = 45%, so passed in both = 55%. The trap is forgetting to subtract the overlap and answering 45%. Draw the two-circle picture once in your rough sheet if the wording looks messy.

Income, expenditure and savings

Savings questions get people because a small change in expenditure produces a large change in savings. Suppose someone earns 50,000 and spends 80% of it, so the saving is 10,000. If income rises by 20% and expenditure rises by 10%, income is 60,000, expenditure is 40,000 x 1.1 = 44,000, and savings become 16,000. That is a 60% rise in savings, on a 20% income rise.

The lesson: work with actual numbers (100, or a friendly number like 50,000) and never with percentages of percentages. Set income = 100, expenditure = 80, savings = 20. Income becomes 120, expenditure 88, savings 32, a 60% rise. The percentages are the same and the numbers are small. Picking the base as 100 or as a number that makes all the percentages come out whole is the most useful habit in this chapter.

Assuming a convenient base

This is a technique that deserves its own heading. When a question gives only percentages and no absolute numbers, assume a base that makes the arithmetic painless.

• If percentages involve 20% and 25%, use 100 or 200.
• If they involve 12.5% or 37.5%, use 80 or 160 (or 8, 16, 24).
• If they involve 33.33% or 16.67%, use 60, 120 or 300.
• If they involve 1/7, use 70 or 140.

If the question asks for a final percentage, your assumption never changes the answer. If the question asks for an absolute number, it will always give you one fixed number somewhere to scale against.

Here is an example. "A number is first increased by 25%, then decreased by 20%, and finally increased by 40%. What is the net change?" Assume the number is 100. Rises to 125, then falls by 20% (a fifth) to 100, then rises 40% to 140. Net change is 40%. You can see the trick: 25% up followed by 20% down cancels exactly (this is the price-and-consumption pair from earlier), so only the last 40% survives.

The 'find the number' questions

These say something like: "25% of a number is 45 more than 12.5% of it. Find the number." The equation is 25% of x minus 12.5% of x = 45, which means 12.5% of x is 45, which means x/8 = 45, so x = 360. Check: 25% of 360 = 90, 12.5% of 360 = 45, and 90 - 45 = 45. Correct.

For nested percentages, multiply the fractions. What is 30% of 40% of 500? It is 0.3 x 0.4 x 500 = 60. Or 40% of 500 is 200, and 30% of 200 is 60. If the two percentages are nice fractions, like 25% of 40%, you get 1/4 x 2/5 = 1/10, which is 10%.

Mixtures and populations in the percentage frame

Two more types show up in mocks and previous papers regularly.

First, mixtures: "A 40-litre solution has 25% acid. How much water should be added to make it 20% acid?" The acid stays the same at 10 litres. For 20% (which is 1/5) to hold, the total must be 50 litres, so 10 litres of water goes in. The trick is to hold the constant quantity fixed and change the total, not to recompute both. A "which quantity stays fixed?" question is the entire chapter of mixtures in disguise.

Second, population: a growth of r% per year for n years is a compound interest formula in disguise, and the a + b + ab/100 rule is the same as the two-year compound interest rule. If you have gone through the profit and loss shortcuts, you will notice the same successive-percentage idea working there as well.

Percentage in data interpretation

In DI sets, percentages are the main calculation, and the fraction table is what makes the section finishable. If a bar chart shows 45 out of 60 and you are asked for the percentage, you say 3/4 = 75% instantly. If it shows 18 out of 72, that is 1/4 = 25%. If it shows 35 out of 56, divide both by 7 to get 5/8 = 62.5%.

A few DI habits that pay off:

• Compare fractions instead of computing percentages. Is 14/40 bigger than 17/50? Cross-multiply: 14 x 50 = 700 and 17 x 40 = 680. So 14/40 is bigger. You did not need a single percentage.
• For percentage change, do (change / old) instead of (change / new). The base is always the "from" value.
• Round aggressively when the options are far apart. If the four options are 12%, 18%, 25% and 30%, an answer that comes to about 17.6% is 18%. Do not spend 30 seconds on the second decimal.

More on this is in the post on data interpretation tricks.

A short list of relations to keep in your head

None of these need to be derived in the exam. They are all consequences of what you have already read.

• If A is x% more than B, then B is (100x)/(100 + x)% less than A. Example: x = 25 gives 2500/125 = 20%.
• If A is x% less than B, then B is (100x)/(100 - x)% more than A. Example: x = 20 gives 2000/80 = 25%.
• If the price of an item rises by x%, consumption must fall by (100x)/(100 + x)% to keep expenditure unchanged.
• If the side of a square rises by x%, the area rises by 2x + x^2/100 percent.
• If two quantities change by x% and y% and their product is asked, the change is x + y + xy/100.
• If x% of A equals y% of B, then A : B = y : x.

The last one is neat and rarely used. If 20% of A equals 30% of B, then A : B = 30 : 20 = 3 : 2. Check with numbers: A = 300, B = 200, 20% of 300 = 60, 30% of 200 = 60. Correct.

The mistakes that cost marks

I have seen the same errors in almost every mock analysis. The first is applying the second percentage to the original base instead of the changed base. It is the entire reason the successive-change rule exists. Two 10% increases are not 20%, they are 21%.

The second is reading "more than" and "of" carelessly. "A is 25% more than B" and "B is 25% less than A" are not the same statement. One is true and the other is false. When you finish a question, say the relation back to yourself in words: "so A is 5/4 of B, which means B is 4/5 of A, which is 20% less." That ten-second check catches most of these errors.

The third is over-calculating when options are wide apart. Percentage questions are the best place to practise estimation. If you have spent more than 60 seconds on a percentage question that was not multi-step, stop and reread; you likely missed a fraction.

The fourth is skipping the fraction table in the first month. Some students think it is childish and try to calculate everything. They can do it, but their speed plateaus. The students who memorise the table are the ones whose section timings quietly improve.

The fifth is mixing up percentage points and percent. If a bank's interest rate goes from 8% to 10%, it rose by 2 percentage points, but it rose by 25% in relative terms (2/8). DI and banking papers do test this distinction.

How to actually practise this

Do not read this chapter once and move on. A workable plan for the first two weeks looks like this.

Week one, mornings: 15 minutes on the fraction table. Cover the percentages, look at each fraction and say the percentage aloud; then the reverse. Do it until you never hesitate. In the evening, do 25 percentage questions from a standard book, timed at 40 seconds each, and only mark which ones you took longer than the limit on.

Week one, evenings: rewrite the solutions of the slow ones with the fraction method. Do not just read the solution; redo the question with fractions in the margin.

Week two: mix in successive-change questions, price-consumption questions, and election questions. Aim for 30 questions a day in 20 minutes. After every 10 questions, look for the pattern in the ones you got wrong. Nine times out of ten it is "base confusion" (which quantity is the percentage of?).

At the end of the second week, take a sectional test rather than another 100 questions. The free sectional practice on Pareeksha lets you attempt a set of quant questions under a timer, and the percentile after a full mock test shows where you stand against other candidates. What you are looking for is not a big score, but whether the percentage questions now take you 25 to 40 seconds instead of a minute. If they do, move on to profit and loss and time and work, which lean on exactly the same fraction thinking.

A worked timing example

A concrete illustration of what "fast" looks like. Question: "The price of sugar rises by 25%. A family wants to keep its spending on sugar the same. By what percent must it cut consumption?"

Slow way: assume price = 100, quantity = 100, spend = 10,000. New price 125. New quantity = 10,000/125 = 80. Cut = 20%. About 45 seconds if you write everything.

Fast way: 25% is 1/4. Reverse is 1/5, which is 20%. Three seconds.

Question: "In a class, 60% are girls. If 25% of the girls and 40% of the boys wear glasses, what percent of the class wears glasses?" Assume 100 students: 60 girls, 40 boys. 25% of 60 = 15, 40% of 40 = 16. Total = 31, so 31%. You can do this in your head in about 15 seconds because 25% is a quarter and 40% of 40 is 16 (two-fifths of 40).

Question: "A shopkeeper marks up a product 20% above cost and gives a 10% discount. What is the profit or loss percent?" 1.2 x 0.9 = 1.08, so 8% profit. That is the same rule as a successive change, and you can read it in two seconds if you have absorbed the rule. This is why percentage feeds directly into profit and loss.

Where percentage appears in each exam family

The syllabus lists change with each notification, so I will not give you fixed weightage numbers here. What I can say from looking at past papers is the shape. In SSC papers, percentage often appears directly, usually alongside profit and loss and ratio, and it is tested indirectly through data interpretation. In RRB NTPC and Group D papers, it appears in simplified forms, often as a stand-alone question worth attempting first. In IBPS and SBI papers, the direct question is rarer but it powers the arithmetic in DI, quantity comparisons and approximation. In all of them, the fraction table is the same. If you are preparing for more than one exam, you do not need separate percentage prep. See the note on preparing two exams together for how to share the quant work.

If you want to see how many questions from this chapter appear where, the honest approach is to look at the last three years of your target exam's papers, count them yourself, and treat what you find as more reliable than any "weightage" chart. The maths chapter weightage post lays out how to do that count.

What not to do

Do not memorise formulas without checking them once with numbers. Every rule above can be tested on 100 in ten seconds, and tests build trust in the rule. If you cannot recall a formula in the exam, you can always rebuild it by assuming 100.

Do not skip the "of what?" check. Percentage errors are almost never arithmetic; they are almost always base errors.

Do not use a calculator-style long-multiplication approach for numbers like 12.5% or 37.5%. The exam will not give you a calculator in most of these papers, and even where an on-screen one is offered, it is slower than the fraction.

Do not spend hours on a hard percentage question in the exam. The chapter has enough easy questions that you can afford to skip the two that look tangled. Mark them, come back if time is left.

Your next step

Print the fraction table today. Tomorrow morning, spend fifteen minutes on it. Then do 20 timed percentage questions and mark any that took more than 45 seconds. Those are your notes for the week. Once you can do them comfortably, take the free mini-mock on Pareeksha and check how your quant section time compares with the rest of the paper.

FAQ

Is the fraction table enough, or do I need all the formulas? The table plus the successive change rule (a + b + ab/100) covers most of the direct questions. The rest are consequences you can rebuild by assuming 100.

How many percentage questions should I practise before moving on? Around 150 to 200 well-reviewed questions is enough for most people, provided you review the slow ones. Quality of review matters more than the count.

Should I use 100 as the base every time? Use 100 when the question has only percentages. If the percentages are 12.5% or 37.5%, use 80 or 160 instead, so the numbers stay whole. If an absolute number is given, use that.

What if I get the answer in decimals and the options are whole numbers? Recheck the base. Most of the time you have used the wrong denominator (for example, computing "percent more" against the larger number).

Is percentage the same in SSC and bank exams? The concepts are the same. Bank exams tend to bury percentage inside data interpretation and approximation, so you need the fraction table to be even more automatic there.

Can I skip the fraction table if I am good at mental maths? You can try, but you will still spend time on cases like 7.69% or 14.28%. The table costs a week; the time it saves over the full course of preparation is much larger.