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📚 Part of: Percentages guide

Reverse Percentage: Finding the Original Number

The sale tag shows the after. CLAT asks for the before. One division gets you there, and one lazy subtraction gets you a wrong option that is waiting for you.

RR ✔ Reviewed by Ravi Raj Singh · BTech (Computer Science); MA English, NET-qualified
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past CLAT Qs solved
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📑 On this page
⚡ The short answer
Reverse percentage finds the original value when you only know the value after a percentage change. The final is the original times a multiplier: (1 + r/100) after a rise, (1 − r/100) after a fall. So Original = Final ÷ multiplier. Never add or subtract the same % back: it was taken on a different base.
🎬 The 30-second story
The 20% off phone
1
“Flat 20% off! I got it for ₹15,200!”
📱
Meher
Meher buys a phone in the festive sale.
2
“Easy. Add 20% back: ₹18,240.”
🧮
Aarav
Aarav, in two seconds flat.
3
“20% off ₹18,240 is ₹14,592. Not what she paid.”
🏷️
Zoya
Zoya runs it forwards.
4
“₹15,200 is 80% of the price. ₹15,200 ÷ 0.8 = ₹19,000.”
✅
Zoya
And ₹19,000 minus 20% is exactly ₹15,200.
Tara's maths: The 20% was taken on the old price, ₹19,000, so the discount was ₹3,800. Aarav used the new price as the base and came up ₹760 short. In reverse questions the percentage belongs to the number you don't know yet.

What is reverse percentage, and why can't you just add the % back?

Every percentage has an owner: the base it was taken on. In a reverse question you walk back from the end, but the percentage still belongs to the start, the one number you don't have. So treat the change as a multiplier: a 20% cut means new = 0.8 × old. To undo "times 0.8", divide by 0.8. That's the whole topic.

🟦 Picture the percent
The 100-square method: what is one square worth?
Paid after 20% off
80 squares = ₹15,200
so 1 square = ₹190
Original price
100 squares = 100 × ₹190
= ₹19,000

What is the formula to find the original value?

🧮 The formula
Reverse percentage in one line
🧾
Final value
the number you can see
÷
✖️
Multiplier
1 + r/100 (rise) or 1 − r/100 (fall)
=
🎯
Original value
the number CLAT asks for
⚔️ Side by side
Forward percentage vs reverse percentage
➡️Forward
You know the start
  • •₹19,000 × 0.8 = ₹15,200
  • •The % is of the number you hold
⬅️Reverse
You know the end
  • •₹15,200 ÷ 0.8 = ₹19,000
  • •The % is of the number you are hunting
TestForwardReverse
25% rise× 1.25÷ 1.25
25% fall× 0.75÷ 0.75

Same multiplier, opposite operation.

It wears three costumes. Before-and-after: a price after a change. Part-to-whole: food is 23% of a budget and costs ₹12,880, so the budget is 12,880 ÷ 0.23. Gap-to-whole: two groups at 17.25% and 14.25% differ by 15.75 million, so 3% of the whole is 15.75 million.

How do you solve reverse percentage questions step by step?

✍️ Worked example Warm-up ⏱ 20 sec
The food-delivery bill
Rohan's biryani order costs ₹630 including 5% GST. What was the food price before tax?
  1. 1
    GST is added on the food price, so the bill is 105% of it.
  2. 2
    Food price = 630 ÷ 1.05 = ₹600.
  3. 3
    Check: ₹600 + 5% = ₹630. ✔
Answer: ₹600
⚡ The exam-hall shortcut
÷1.05 is ×20/21: 630 ÷ 21 = 30, × 20 = 600. Knocking 5% off ₹630 gives ₹598.50: close, and wrong.
✍️ Worked example CLAT level ⏱ 30 sec
The follower drop
After an unpopular post, Zoya's account lost 12.5% of its followers and now has 7,000. How many did it have before?
  1. 1
    A 12.5% fall leaves 87.5%, i.e. 7/8 of the original.
  2. 2
    7 parts = 7,000, so 1 part = 1,000 and 8 parts = 8,000.
  3. 3
    Check: 1/8 of 8,000 is 1,000 lost, leaving 7,000. ✔
Answer: 8,000 followers
⚡ The exam-hall shortcut
See 12.5%, think eighths: final × 8/7. The trap, 7,000 + 12.5% = 7,875, will be in the options.
⚠️ Adding the % back always lands on the wrong side
After a fall, final + r% is always too small (₹18,240, not ₹19,000). After a rise, final − r% is too small too (₹598.50, not ₹600). Expect that number among the options.
🎛️ Try it yourself — change any number
Reverse it yourself
Original value
19,000
Change in units
−3,800
15,200 ÷ 0.8 = 19,000
It opens on Meher's phone: ₹15,200 after −20% gives ₹19,000. Try 7,000 with −12.5%, then 883 with +54% (CLAT 2023).

How do you reverse two or more percentage changes?

Several changes? Multiply the multipliers into one and divide once, or peel them off from the last to the first. For Kabir's watch below: ₹17,600 ÷ 0.8 = ₹22,000, then ÷ 1.1 = ₹20,000.

✍️ Worked example CLAT level ⏱ 40 sec
Hike, then sale
Kabir raises a smartwatch's price by 10%, then offers 20% off the new price. A customer pays ₹17,600. What was the price before the hike?
  1. 1
    Combined multiplier = 1.1 × 0.8 = 0.88, a net 12% fall.
  2. 2
    Original = 17,600 ÷ 0.88 = ₹20,000.
  3. 3
    Check: ₹20,000 × 1.1 = ₹22,000; 20% off that is ₹17,600. ✔
Answer: ₹20,000
⚡ The exam-hall shortcut
Netting it as −10% gives 17,600 ÷ 0.9 = ₹19,555.56, a distractor.
✍️ Worked example Tricky ⏱ 60 sec
The salary that ran out
Meher's cousin spends 30% of her salary on rent, then 25% of what is left on food, and has ₹21,000 remaining. What is her salary?
  1. 1
    After rent, 70% is left (×0.7). Food takes 25% of that, so 75% survives (×0.75).
  2. 2
    Remaining = 0.7 × 0.75 = 0.525 of the salary.
  3. 3
    Salary = 21,000 ÷ 0.525 = ₹40,000.
  4. 4
    Check: rent ₹12,000 leaves ₹28,000; food ₹7,000 leaves ₹21,000. ✔
Answer: ₹40,000
⚡ The exam-hall shortcut
"Of what is left" is successive. Adding 30% + 25% gives 21,000 ÷ 0.45 = ₹46,666.67, a trap.
📌 Order matters only when a flat amount sneaks in
A subtotal gets a ₹40 delivery fee, then 5% GST on everything: bill ₹693. Undo the last step first: 693 ÷ 1.05 = 660, then 660 − 40 = ₹620. Subtracting ₹40 first gives ₹621.90, which is wrong.

What is the fastest way to find the original in the exam?

Dividing by a fraction is multiplying by its flip, and most CLAT percentages are friendly fractions. Learn the right-hand column.

ChangeMultiplierOriginal = Final ×
+25%5/44/5
+20%6/55/6
+12.5%9/88/9
+50%3/22/3
+5%21/2020/21
−20%4/55/4
−25%3/44/3
−12.5%7/88/7
−10%9/1010/9
→ scroll to see more
💡 Estimate, then let the options finish it
CLAT 2023: 883 after a 54% rise. 1.54 ≈ 1.5, so the original is a bit under 883 × 2/3 ≈ 589. Only 573 fits. If two options are close, plug back: multiply each by the multiplier and see which hits the final.

How does reverse percentage hide in a CLAT caselet?

CLAT rarely says "find the original". It gives a paragraph of shares, then one real number in the question. Spot its slice and climb to the whole, as in the 2021 population caselet.

📊 The data
CLAT 2021: share of the state's population by age group
0–15 · below 36
30%
16–25 · below 36
17.75%
26–35 · below 36
17.25%
36–45
14.5%
46–55
14.25%
56–65
5.12%
66+
1.13%

Q142 gives the three 'below 36' bars (65%); Q144 gives the gap between 26–35 and 46–55 (3 points).

🧭 Decision flow
Which reverse question is this?
❓ Do you know a value after a % change?
Yes →
Original = final ÷ (1 ± r/100)
No ↓
❓ Do you know a part and its % share?
Yes →
Whole = part ÷ (share/100)
No ↓
❓ Do you know the gap between two shares?
Yes →
Whole = gap ÷ (difference in shares/100)
No ↓
❓ Is it "A is x% more than B" and you know A?
Yes →
B = A ÷ (1 + x/100)
No →
No base? Likely cannot be determined.

"More than" questions run backwards too

Kabir sells 25% more on Sunday than Saturday; Sunday brings ₹9,000. Saturday = 9,000 ÷ 1.25 = ₹7,200, not 9,000 × 0.75. And Saturday is 1,800 ÷ 9,000 = 20% less, not 25%: the base changed.

Which reverse percentage traps cost the most marks?

How did CLAT ask reverse percentage?

📝 Asked in CLAT 2023 · Q141 Original from growth
World fruit production went up 54 percent between 2000 and 2019, to 883 million tonnes. Five fruit species accounted for 57 percent of the total production in 2019, down from 63 percent in 2000. Use the data in the passage to answer the following questions.

What was the world fruit production in 2000?

A474 million tonnes
B517 million tonnes
C573 million tonnes
D406 million tonnes
Reveal answer + reasoning
Answer: C
883 is the 2019 figure, after a 54% rise. So 883 = 2000 value × 1.54, and the 2000 value = 883 ÷ 1.54 = 573.4 million tonnes. Plug-back: 573 × 1.54 = 882.4 ≈ 883. Time: 30 seconds.
Why the others fail
  • A — 474 × 1.54 = 730.
  • B — 517 × 1.54 = 796.
  • D — 406 is 883 × 0.46: knocking 54% off the 2019 figure, the classic trap.
📝 Asked in CLAT 2021 · Q142 Whole from a group of slices
… the state's 30 per cent of the population were children between the age group of 0-15. Next to child population, 17.75 per cent of the population were adolescents between the age group of 16 and 25. The early adult population, i.e., the age groups 26 to 35 were 17.25 per cent, 36 to 45 were 14.50 per cent, respectively. The population who are between the age group of 46 to 55 constitute 14.25 per cent and the elderly population of the state, i.e., 56 to 65 (5.12%) and 66 above (1.13%)…

There are 400 million people below 36 years. How many million (approx.) people are in the age group 56-65?

A32.72 million
B25.75 million
C31.50 million
D59.30 million
Reveal answer + reasoning
Answer: C
"Below 36" covers 0–15, 16–25 and 26–35: 30 + 17.75 + 17.25 = 65%. So 65% of the total is 400 million, and total = 400 ÷ 0.65 = 615.4 million. The 56–65 group is 5.12% of that: 31.5 million. Faster: 400 × 5.12/65 = 31.5. Time: 45 seconds.
Why the others fail
  • A — Needs an under-36 group of about 415 million, not 400.
  • B — Implies an under-36 group of about 327 million.
  • D — Needs a total over 1,150 million.
📝 Asked in CLAT 2021 · Q144 Whole from a gap
Same caselet: … the age groups 26 to 35 were 17.25 per cent … The population who are between the age group of 46 to 55 constitute 14.25 per cent …

If the difference between the number of people in the age groups 46-55 and 26-35 is 15.75 million, then total population of the state is approximately?

A360.23 million
B390 million
C400 million
D525 million
Reveal answer + reasoning
Answer: D
26–35 is 17.25% and 46–55 is 14.25%, so their gap is 3% of the total. 3% of total = 15.75 million, so total = 15.75 ÷ 0.03 = 525 million. Check: 3% of 525 = 15.75. ✔ Time: 25 seconds.
Why the others fail
  • A — 3% of 360.23 is about 10.8 million, not 15.75.
  • B — 3% of 390 is 11.7 million.
  • C — 3% of 400 is 12 million.
📝 Asked in CLAT 2025 · Q109 "% more than" reversed (disputed key)
… As of 2020-21, Tamil Nadu has the highest gender wage gap among agriculture field laborers at 112 per cent. It is followed by Goa (61 percent) and Kerala. The wage gap is the lowest in Jharkhand and Gujarat (6 percent each), but the women laborers there get paid just Rs. 239 and Rs. 247 per day, respectively…

If the wages paid to men working in agricultural sector in Goa are Rs. 335 on an average, what is the amount of wages paid to women in the region?

ARs. 204 approx.
BRs. 330 approx.
CRs. 239 approx.
DNone of these
Reveal answer + reasoning
Answer: A
Tamil Nadu's gap is 112%, and a gap measured on men's wages can't pass 100%. So the base is the women's wage: Goa's men earn 61% more than women. Men = 1.61 × women, so women = 335 ÷ 1.61 ≈ ₹208. The official key says A (₹204), which is 335 × 0.61, a forward reading. So D is arguable. In the hall, A is the nearest option and the key's choice: mark it. Time: 40 seconds.
Why the others fail
  • B — Barely below the men's ₹335; it ignores a 61% gap.
  • C — Jharkhand's women's wage, lifted from the passage as a decoy.
  • D — Strictly, ₹208 is not ₹204, so D has a case. The key rejects it.

Myths, quiz and the cheat sheet

💥 Myth vs fact
Reverse percentage: myth vs fact
🙅 Myth
To undo a 20% rise, take 20% off.
Tap to bust it →
✅ Fact
Take off 20/120 = 16⅔%. ₹120 − 20% is ₹96, not ₹100.
🙅 Myth
Reverse % only means "price before discount".
Tap to bust it →
✅ Fact
It is also part to whole and gap to whole, as in the 2021 caselet.
🙅 Myth
You must divide exactly in the exam.
Tap to bust it →
✅ Fact
Flip a friendly fraction, estimate, then plug the closest option back.
🎯 Quick quiz
Five reverse questions, one rule
0 / 5
Sneakers on a 30% sale now cost ₹2,800.

Q1. What was the price before the sale?

After a 60% jump, a creator's monthly views are 4.8 lakh.

Q2. What were the views before the jump?

A fest spends 40% of its budget on the stage, then 25% of the rest on food, leaving ₹1,35,000.

Q3. What was the total budget?

Rohan scored 20% more than Aarav. Rohan scored 84.

Q4. What did Aarav score, and how much less than Rohan is that in %?

A startup's revenue grew 25% from 2023 to 2024. Its 2024 profit was ₹50 lakh.

Q5. What was its 2023 revenue?

🎯 Reverse percentage in a nutshell
  • The percentage belongs to the original, the number you don't have yet.
  • Original = final ÷ (1 + r/100) after a rise, final ÷ (1 − r/100) after a fall.
  • Several changes: multiply the multipliers, divide once.
  • Part to whole: whole = part ÷ share. Gap to whole: whole = gap ÷ difference in shares.
  • Estimate, then plug options back.
📎 Formula card
  • After an r% rise: Original = Final ÷ (1 + r/100)
  • After an r% fall: Original = Final ÷ (1 − r/100)
  • Two changes: Original = Final ÷ [(1 + a/100)(1 + b/100)]
  • Part to whole: Whole = Part ÷ share. Gap: Whole = Gap ÷ share difference
  • A is x% more than B: B = A ÷ (1 + x/100); B is x/(100 + x) × 100 % less
  • Flips: ÷1.25 = ×4/5 · ÷1.2 = ×5/6 · ÷1.125 = ×8/9 · ÷0.8 = ×5/4 · ÷0.75 = ×4/3 · ÷0.875 = ×8/7

Frequently asked questions

How do you find the original price after a discount?
Turn the discount into what is left. After a 20% discount you pay 80% of the original, so divide the sale price by 0.8. A phone sold for ₹15,200 after 20% off cost ₹15,200 ÷ 0.8 = ₹19,000 before the sale.
What is the reverse percentage formula?
Original = Final ÷ (1 + r/100) after an increase of r%, and Original = Final ÷ (1 − r/100) after a decrease. The bracket is the multiplier that made the final, so dividing by it undoes the change. For several changes, multiply the multipliers and divide once.
Why can't I just subtract the percentage to find the original?
Because the percentage was calculated on the original, not on the final. A 25% rise turns 80 into 100. Taking 25% off 100 gives 75, not 80, since 25% of 100 is bigger than 25% of 80. Subtracting it back always uses the wrong base.
How do you find the total when a percentage share is given?
Treat the known part as the final value and its share as the multiplier. If food is 23% of a budget and costs ₹12,880, the budget is 12,880 ÷ 0.23 = ₹56,000. Given a gap between two shares, divide the gap by the difference in their percentages.

Keep going

← Previous topic
Successive Percentage Change: the a + b + ab/100 Rule
Why +50% then −50% leaves you down 25%, and the one-line fix
Next topic →
Population Growth and Depreciation
Why 20% a year never makes anything worthless, and the one formula
📚
Part of the chapter
Percentages for CLAT Quantitative Techniques
See how this topic fits the whole of Percentages →

Connected topics in other chapters

Percentage Increase, Decrease and "% More Than"
Reverse % is percentage change run backwards. Same base rule, opposite direction.
Successive Percentage Change
Undoing two changes needs the combined multiplier from the a + b + ab/100 rule.
Budgets and Pie Charts
"If food is ₹X, what is the total budget?" is a reverse % question in a pie.
Marked Price and Discount
Finding the marked price from the sale price is the most common reverse % in the wild.
Caselet DI
Where CLAT hides reverse % questions: a paragraph of shares and growth rates.

Every topic in Percentages

  1. 1.Fractions, Decimals and Percents: One Number, Three Outfits
  2. 2.Percentage Increase, Decrease and "% More Than"
  3. 3.Successive Percentage Change: the a + b + ab/100 Rule
  4. 4.Reverse Percentage: Finding the Original Number (you're here)
  5. 5.Population Growth and Depreciation
  6. 6.Percentage Points vs Percent: Two Answers, One Change
  7. 7.Budgets and Pie Charts: Percentage Share
  8. 8.Caselet DI: Turning a CLAT Quant Passage into a Table
  9. 9.Percentage Shortcuts and Approximation

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