Percentage Shortcuts: Master Fraction Equivalents and Base-Change Tricks for SSC and Bank Exams

Quick Answer: The two percentage shortcuts every SSC and Bank aspirant must master are fraction equivalents (1/8 = 12.5%, 1/6 = 16.66%, 1/3 = 33.33%) and the base-change trick (if A is x% more than B, B is not x% less than A — you divide by the new base). Combine these with the successive change formula a + b + ab/100, and most percentage questions collapse into 20-second mental math.

Why Percentages Decide Your SSC & Bank Exam Score

Percentage is not just one chapter of quantitative aptitude — it is the foundation underneath profit and loss, simple and compound interest, data interpretation, and mixture problems. In SSC CGL and SSC CHSL Tier-I, direct percentage questions typically contribute 1–2 questions out of 25 maths questions, but the concept powers another 8–10 questions across arithmetic and DI. In IBPS PO and SBI PO prelims, data interpretation sets (usually 10–15 questions) are essentially percentage application in disguise.

The real differentiator is speed. SSC CGL Tier-I gives you roughly 60 seconds per question across all sections, and prelims-level Bank exams are even tighter. A candidate who converts 16.66% to 1/6 mentally saves 30–45 seconds per question over one who multiplies by 16.66 on paper. Across a 25-question section, that is the difference between attempting 18 questions and attempting 23 — often the difference between selection and cutoff failure. Official exam patterns and notifications are published on ssc.gov.in and ibps.in, and both confirm the tight time-per-question arithmetic above.

Fraction Equivalents Table: Memorise Once, Use Forever

Every “awkward” percentage in exams is actually a fraction in disguise. Examiners deliberately use 12.5%, 16.66%, and 8.33% because strong candidates instantly see 1/8, 1/6, and 1/12 — while weak candidates reach for long multiplication. Memorise this table once; it serves you in every exam for life.

Also memorise the multiplicative forms: an increase of 25% means multiplying by 5/4; a decrease of 16.66% means multiplying by 5/6. These “multiplier fractions” turn chained percentage problems into a single line of cancellation.

How to Convert Percentages to Fractions in 2 Seconds

The method is one step: write the percentage over 100 and simplify.

1. Put the percentage as a fraction: 12.5% = 12.5/100
2. Clear the decimal: 125/1000
3. Simplify: 125/1000 = 1/8. Done.

Exam-style examples:

• 16.66% → 16.66/100 ≈ 1666/10000… but instantly recognisable as 1/6 (since 1/6 = 0.1666…).
• 37.5% → 375/1000 = 3/8.
• 6.25% → 625/10000 = 1/16.
• 8.33% → 1/12, and 14.28% → 1/7 (from the repeating pattern 142857).

With the table memorised, you skip all three steps — you see 12.5% and your hand writes 1/8 automatically.

Using Fraction Equivalents to Crack Exam Questions Fast

Example 1 (SSC CGL type): Find 12.5% of 648.

Decimal method: 648 × 0.125 — slow on paper. Fraction method: 648 × 1/8 = 81. Two seconds.

Example 2: A number is increased by 16.66%. If the original number is 432, find the new number.

Increase of 16.66% = multiplier 7/6. New number = 432 × 7/6 = 72 × 7 = 504. No decimal, no approximation.

Example 3 (Bank PO type): In an exam, 33.33% of 960 candidates failed. How many passed?

Failed = 960 × 1/3 = 320. Passed = 640. The 33.33% is deliberately planted to reward the fraction reflex.

Example 4: A shopkeeper offers a discount of 14.28% on an item marked at ₹1,400. Find the discount.

14.28% = 1/7. Discount = 1400/7 = ₹200. Compare this with computing 1400 × 0.1428 by hand — a 30-second saving.

Base-Change Trick: When the Base Shifts

This is the single most tested percentage trap in SSC and Bank exams. Percentages are always calculated on a base, and when the base changes, the percentage changes.

Statement: A is 20% more than B. By what percent is B less than A?

Wrong answer: 20%. Right answer: 20/120 × 100 = 16.66% (which is 1/6 — your fraction table again).

The rule:

• If A is x% more than B, then B is [x/(100+x)] × 100 % less than A.
• If A is x% less than B, then B is [x/(100−x)] × 100 % more than A.

Fast fraction version: “20% more” = multiplier 6/5 (A/B = 6/5). To reverse, flip: B/A = 5/6, which is a decrease of 1/6 = 16.66%. Whenever the multiplier is a clean fraction, the reverse percentage is simply the reciprocal’s shortfall — pure mental math.

Verification example: Let B = 100. A = 120. B (100) is less than A (120) by 20. As a percentage of A: 20/120 = 1/6 = 16.66%. Confirmed.

Successive Percentage Change Formula: a + b + ab/100

When two percentage changes happen one after another, you cannot simply add them — each acts on a different base. The shortcut formula:

Net change % = a + b + (ab)/100

Sign rules:

• Increase → positive sign (e.g., +10)
• Decrease → negative sign (e.g., −10)
• Substitute with signs; a negative net result means an overall decrease.

Example: +10% then −10% → 10 − 10 + (10 × −10)/100 = 0 − 1 = −1%, i.e., a net 1% decrease — never 0%.

For three changes, apply the formula twice: first combine a and b, then combine that result with c.

Solving Successive Change Problems in Under 20 Seconds

Timed Example 1: A price increases by 12.5% and then decreases by 8.33%. Find the net change.

Decimal method: painful. Fraction method: increase of 12.5% = multiplier 1 + 1/8 = 9/8. Decrease of 8.33% = multiplier 1 − 1/12 = 11/12. Net multiplier = 9/8 × 11/12 = 99/96 = 33/32 = 1 + 1/32. Net change = +1/32 = +3.125%. Under 20 seconds with practice.

Timed Example 2: A number is increased by 20% and then decreased by 10%. Net change?

Formula: 20 − 10 + (20 × −10)/100 = 10 − 2 = +8%. Or fraction check: 6/5 × 9/10 = 54/50 = 1.08. ✓

Timed Example 3: Population rises 10%, then 20%, then falls 4.16% (≈ 1/24). Net?

Multiply multipliers: 11/10 × 6/5 × 23/24 = (11 × 6 × 23)/(10 × 5 × 24) = 1518/1200 = 1.265, i.e., 26.5% increase. The odd-looking 4.16% is a planted fraction (1/24), designed to be fast only for table-holders.

Common Mistakes Aspirants Make with Percentages

• Adding percentages on different bases: “25% increase then 25% decrease = 0%” is wrong. Net = 25 − 25 − 625/100 = −6.25%.
• Base confusion in comparison: Treating “A is 20% more than B” as reversible. It is not — B is only 16.66% less than A.
• Sign errors in successive change: Forgetting the negative sign on b in a + b + ab/100 when the second change is a decrease.
• Rounding 16.66% as 17% in intermediate steps — in multi-step problems the error compounds. Always use 1/6.
• Multiplying instead of dividing in reverse-percentage questions: “After a 25% increase the value is 500” → original = 500 ÷ 5/4 = 400, not 500 × 0.75.

Practice Set: 10 Exam-Style Questions with Solutions

1. Find 37.5% of 480. → 3/8 × 480 = 180.
2. A number increased by 14.28% becomes 720. Find the number. → Multiplier 8/7. Number = 720 × 7/8 = 630.
3. If A is 25% more than B, B is what percent less than A? → 25/125 = 1/5 = 20%.
4. Price rises 20% then falls 20%. Net change? → 20 − 20 − 400/100 = −4%.
5. Two successive discounts of 10% and 20% equal a single discount of? → −10 − 20 + 200/100 = −28%, i.e., 28% discount.
6. Find 62.5% of 640. → 5/8 × 640 = 400.
7. A’s salary is 16.66% less than B’s. By what percent is B’s salary more than A’s? → A/B = 5/6; B/A = 6/5 → 1/5 = 20% more.
8. Population increases by 8.33% and then by 6.25%. Net increase? → 13/12 × 17/16 = 221/192 ≈ 1.1510 → 15.1% (exactly 29/192 = 15.104%).
9. A score of 360 is 33.33% more than what number? → 360 = x × 4/3 → x = 270.
10. Rice price rises 25%; by what percent must consumption fall to keep expenditure unchanged? → Base-change: 25/125 = 20%.

Memorisation Plan and Revision Schedule

A seven-day plan to convert the table into reflex:

• Day 1: Memorise halves to fifths (1/2 to 4/5). Write each three times, say each aloud.
• Day 2: Add sixths, sevenths, eighths (1/6, 1/7, 1/8 and multiples of 1/8).
• Day 3: Add ninths to sixteenths (1/9, 1/10, 1/11, 1/12, 1/16).
• Day 4: Learn multiplier fractions for increases and decreases (25% up = 5/4, 16.66% down = 5/6, etc.). Solve 15 questions using only fractions.
• Day 5: Base-change drill — 10 “A is x% more than B” questions, solved mentally.
• Day 6: Successive change drill — 15 questions with the a + b + ab/100 formula, all timed at 25 seconds each.
• Day 7: Mixed timed test of 20 questions in 8 minutes. Review every question where you touched decimal calculation.

After Day 7, refresh with a 5-minute table recital twice a week until exam day. Spaced repetition is what makes the fraction reflex permanent.

Frequently Asked Questions

Q: What is 1/8 as a percentage?

1/8 = 12.5%. The full equivalents chain: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.66%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8.33%, 1/16 = 6.25%.

Q: What is the successive percentage change formula?

Net change = a + b + ab/100, where increases take a positive sign and decreases take a negative sign. A negative result means a net decrease.

Q: If a price increases by 25% and then decreases by 20%, what is the net change?

Apply the formula: 25 + (−20) + (25 × −20)/100 = 25 − 20 − 5 = 0%. The price returns exactly to the original — a classic exam trap because many candidates guess ±5%.

Q: Why is the fraction method faster than decimal calculation in exams?

Fractions allow cancellation and pure mental math — 648 × 1/8 collapses instantly, while 648 × 0.125 needs written work. Per question this saves 20–40 seconds, which across a 25-question section adds up to 8–15 extra minutes of attempt time.

Q: If A is 20% more than B, by what percent is B less than A?

Use the base-change trick: 20/(100+20) × 100 = 20/120 × 100 = 16.66% (1/6). The base has shifted from B to A, so the reverse percentage is smaller.

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