Percentage Tests — Pick a Level and Start
Tap a level to see every test in it. Start at Level 1 the day you learn the fraction equivalents, then move to Level 2 with the timer running — that is where two or three percentage steps get chained inside one question, exactly as the real paper does it.
Level 1 Basic Checking… View tests
One percentage step done cleanly — a conversion, a percentage of a number, a single increase or decrease, a part-of-whole count, one successive pair. The quantity is stated outright and the answer is one or two lines away. Attempt these without the clock while you are still fixing the fraction equivalents in your head.
Level 2 Tier I Standard Checking… View tests
Real SSC CGL Tier I difficulty — three or more linked steps, the quantity built rather than given, or the question run backwards so a result is supplied and a rate is asked. Chains of percent-of relations, a rate charged on a remainder, income and savings both growing, a transfer of votes that reverses a result. This is the score that tells you the chapter is exam-ready.
Percentage is the chapter that decides how the whole arithmetic block goes for you. It carries two or three questions of its own in a typical Tier I shift, but that number badly understates it: profit and loss, discount, simple and compound interest, population growth and most of data interpretation are percentage questions with different vocabulary. A candidate who is fluent here gains time in six other chapters. A candidate who is not loses it in all of them.
What makes the chapter drillable is that the questions repeat in shape far more than in content. A short list of habits — convert awkward rates to fractions, multiply successive changes instead of adding them, read which quantity sits after “percent of” — covers almost everything the commission has asked. These practice tests put twenty-five percentage questions in front of you in one sitting, each with a full solution and the shortcut, in English or Hindi.
How Many Percentage Questions Are Asked in SSC CGL?
Counted directly, percentage is a two-to-three question chapter in Tier I. Counted honestly — including every chapter that is built on it — it touches close to a third of the maths section. That is why it is the chapter to start with if you are beginning chapter wise practice from zero.
| Where it appears | Typical count | What is asked |
|---|---|---|
| Tier I — Quantitative Aptitude | 2–3 | Percentage change, successive change, part-of-whole, income and expenditure |
| Tier II — Mathematical Abilities | 3–5 | Multi-step chains, reverse framings, election shares, population growth |
| Inside profit & loss, discount, interest | 6–8 | Every one of these is a percentage applied to a cost, a marked price or a principal |
| Inside data interpretation | 2–3 | Share of a total, percentage change between two bars, percentage points |
The third and fourth rows are the ones candidates underrate. A discount question is a percentage question; a DI question asking which year grew fastest is a percentage question. Fixing this chapter pays out four times over.
What You Will Practice in the Percentage Chapter
The fraction equivalents worth knowing cold
Almost every awkward rate in an SSC paper is a simple fraction in disguise. Recognising it turns a decimal multiplication into a one-step division.
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33.33% | 3/8 | 37.5% |
| 1/4 | 25% | 5/8 | 62.5% |
| 1/5 | 20% | 7/8 | 87.5% |
| 1/6 | 16.67% | 1/9 | 11.11% |
| 1/7 | 14.29% | 1/12 | 8.33% |
The pattern that matters most: 1/n up is undone by 1/(n+1) down. A rise of 25% (1/4) is cancelled by a fall of 20% (1/5); a rise of 20% by a fall of 16.67%. Half the price-and-consumption questions in the chapter are this one line.
Successive changes multiply — they never add
Two changes of r% and s% applied one after another give a net change of r + s + rs/100 per cent, because the second acts on the figure the first produced. Practically, forget the formula and multiply the factors: a rise of 20% then 25% is 1.2 × 1.25 = 1.5, a rise of 50%. Three consequences follow that questions are built on:
- A rise of
r%then a fall ofr%leaves100 − r²/100per cent, never 100. For 10% that is 99; for 30% it is 91. - The order never matters. Up 25% then down 40% lands exactly where down 40% then up 25% does, because multiplication commutes.
- To undo a combined factor
k, divide by it. Recovering a starting value is always a division, never a subtraction of the netted rate.
Reverse percentage — the commonest single error
If A is x% more than B, then B is x/(100+x) × 100 per cent less than A — not x%. The excess is measured against the smaller quantity and the shortfall against the larger, so the two figures can never match. The pairs worth memorising: 25% more ↔ 20% less, 50% more ↔ 33.33% less, 100% more ↔ 50% less, 20% more ↔ 16.67% less.
The same logic recovers a base. If a value is x% less than an unknown, you reach the unknown by dividing by (100−x)/100. Adding the same percentage back to the smaller figure always falls short.
Income, expenditure and savings
These three are locked together by income = expenditure + savings, which means only two of them can ever carry a rate of their own. Whichever two the question gives rates to, grow those separately and take the third by subtraction. The classic trap is netting the two given rates and applying the difference to the third quantity — meaningless, because the three are different sizes. Setting the income to 100 and working in plain numbers removes the problem entirely.
Price, consumption and spending
Spending is price times consumption, so any one of the three is found by multiplying or dividing the other two — never by adding or subtracting rates. To hold spending level after a price rise of r%, consumption must fall by r/(100+r) × 100 per cent. After a price fall of r%, consumption may rise by r/(100−r) × 100 per cent. When the money is fixed, quantity is inversely proportional to the rate.
Elections and part-of-whole
Election questions are layered percentages: absentees come off the roll, invalid votes come off the votes cast, NOTA comes off the valid votes. Each rate acts on the pool immediately before it, so the surviving fractions multiply. Two readings decide most of these questions:
- With two candidates, the winning margin is the difference of their shares of the valid votes — 58% against 42% is a margin of 16%, not 58%.
- A vote transferred from winner to loser shifts the margin by two; a vote gained from outside shifts it by one. Reading which of the two is described settles the whole question.
For part-of-whole problems the rule is simpler still: pair the count you are given with the percentage that actually describes it, which is often the one the question leaves unstated.
Percentages of areas, volumes and populations
Count how many times each measurement appears. A length appears once, an area twice, a volume three times — so a side multiplier k becomes k² for the area and k³ for the volume. Doubling a radius quadruples a circle’s area; a 10% rise in a sphere’s radius raises its volume by 33.1%. Going the other way, from an area change back to a length, needs a square root — halving the percentage is never valid.
Percentage points versus per cent
A rate moving from 60% to 75% has risen by 15 percentage points, which is a 25 per cent increase. Both are correct answers to different questions, and both are routinely offered as options. Read the wording before dividing.
Solved Examples — SSC CGL Percentage
Example 1 — equal rise and fall. The price of an article is increased by 15% and the new price is then decreased by 15%. What is the net change?
The two do not cancel. Multiply the factors: 1.15 × 0.85 = 0.9775, so the price ends at 97.75% of where it started — a fall of 2.25%. The shortcut is r²/100, and 15²/100 = 2.25. Equal opposite rates always leave a small deficit, never zero.
Example 2 — price and consumption. The price of sugar rises by 25%. By what per cent must a family cut its consumption to keep its monthly spending unchanged?
Spending is price × consumption, so the two multipliers must give 1. The price multiplier is 5/4, so consumption must become 4/5 — a cut of 20%. Note it is not 25%: the rise is measured against the old price and the cut against the old quantity. A rise of 1/n always needs a cut of 1/(n+1).
Example 3 — income and savings. A man saves 25% of his income. If his income rises by 20% and his expenditure by 12%, what per cent of his income does he then save?
Take the income as 100, so savings are 25 and expenditure 75. New income = 120; new expenditure = 75 × 1.12 = 84. New savings = 120 − 84 = 36, and the new rate is 36/120 × 100 = 30%. Savings never carry a rate of their own here — they are whatever the other two leave behind, which is why netting 20 and 12 tells you nothing.
Example 4 — election margin. In an election between two candidates, 10% of the votes polled were invalid. The winner took 60% of the valid votes and won by 3,600 votes. How many votes were polled?
The loser had 40%, so the margin is 60 − 40 = 20% of the valid votes. Valid votes = 3600 × 100/20 = 18,000. Those are 90% of the votes polled, so polled = 18000/0.90 = 20,000. Stopping at 18,000 answers the valid votes — the commonest slip in this family, and it is always offered as an option.
Example 5 — recovering the base. After a reduction, the price of an article is 75% of what it was. By what per cent must the reduced price be raised to restore the original?
Take the original as 100, so the reduced price is 75. It must climb 25, measured against 75: 25/75 × 100 = 33.33%. Answering 25% adds back the same figure that was taken off, but the fall was measured against 100 and the rise against 75 — so the restoring rise is always the larger rate. A fall of 1/4 needs a rise of 1/3.
How the Percentage Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Optional 15-minute timer — the same sectional clock as the real paper, with it to build speed and without it while you are still learning the shortcuts.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Percentage for SSC CGL
- Learn the fraction table before anything else. Every eighth, ninth and twelfth on sight. This single sheet removes most of the arithmetic from the chapter and speeds up profit and loss and interest as well.
- Never add two successive rates. Multiply the factors instead. If you catch yourself writing
20 + 25 = 45, stop — the answer is 50. - Set the stated base to 100. Most word problems become plain arithmetic the moment you do. Read carefully which quantity the question names as the base, because it is not always the one you expect.
- Read the last line before you compute. A large share of wrong answers in this chapter are correct numbers to the wrong question — the valid votes instead of the votes polled, the survivors instead of the loss, the points instead of the per cent.
- Practise the reverse direction deliberately. Tier I increasingly gives you the result and asks for the rate. If you have only ever used a relation forwards, that framing costs a minute you do not have.
- Do Level 1 untimed, the same day you learn the fraction equivalents. The aim is correct method, not speed.
- Move to Level 2 with the 15-minute clock on. That is 36 seconds a question, which is the real Tier I pace. If a three-step percentage chain takes you much over that, you are still deriving rather than recognising.
- Study it before its dependants, not after. Do percentage first, then profit and loss, discount and interest. Each one reuses this chapter wholesale.
- Verify against a real paper. Once Level 2 is consistent, attempt a previous year paper and then a full mock test under locked sectional timing.
SSC CGL प्रतिशत (Percentage) चैप्टर टेस्ट — हिंदी में
प्रतिशत SSC CGL गणित का सबसे उपयोगी अध्याय है। टियर I की एक शिफ्ट में इसके 2–3 प्रश्न सीधे आते हैं, पर असली महत्त्व इससे कहीं अधिक है — लाभ-हानि, बट्टा, साधारण और चक्रवृद्धि ब्याज तथा आँकड़ा निर्वचन, ये सब प्रतिशत पर ही टिके हैं। इसलिए चैप्टरवाइज़ अभ्यास शुरू करने के लिए यही सबसे अच्छा अध्याय है।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (आधारभूत) और लेवल 2 (टियर I स्तर)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।
याद रखने योग्य नियम: क्रमिक प्रतिशत परिवर्तन जुड़ते नहीं, गुणा होते हैं — r + s + rs/100। एक ही दर की वृद्धि और कमी कभी रद्द नहीं होतीं, वे r²/100 प्रतिशत की कमी छोड़ जाती हैं। यदि A, B से x% अधिक है तो B, A से x% कम नहीं बल्कि x/(100+x) × 100 प्रतिशत कम होता है। और मूल्य 1/n बढ़ने पर खर्च स्थिर रखने के लिए खपत 1/(n+1) घटानी पड़ती है।
SSC CGL Percentage — Frequently Asked Questions
How many percentage questions are asked in SSC CGL?
Why do a rise and a fall of the same percentage not cancel?
r% always leave 100 − r²/100 per cent behind — for 20% that is 96, a net fall of 4%.If A is 25% more than B, by what per cent is B less than A?
x% more one way is x/(100+x) × 100 per cent less the other way.The price of a commodity rises by 25%. By what per cent must consumption be cut to keep spending unchanged?
5/4 up needs 4/5 down. A rise of r% needs a cut of r/(100+r) × 100, and a fall of r% allows a rise of r/(100−r) × 100.