Percentages • Topic 4 of 5

Reverse Percentage

Reverse percentage means working backwards from a final value to the original. The single rule: Original = Final ÷ (1 ± x/100). If a price after a 20% discount is ₹480, the original is 480 ÷ 0.8 = ₹600 — students who instead add 20% to 480 get the wrong answer (₹576), the most common CAT trap in this topic. The same logic recovers a pre-tax price, a marked price from a sale price, last year’s population, or a number before a percentage was added. When a quantity is given as "x% more than the answer", divide; when "x% of the answer is known", scale up by the reciprocal fraction.

✅ Solved examples

1. After a 20% discount an item sells for ₹480. Find the marked price.
MP × 0.80 = 480 ⇒ MP = 480/0.8 = ₹600.
2. A number increased by 25% becomes 150. Find the number.
N × 1.25 = 150 ⇒ N = 150/1.25 = 120.
3. A price including 10% tax is ₹770. Find the price before tax.
P × 1.10 = 770 ⇒ P = 770/1.1 = ₹700.
4. After spending 75% of his money a man has ₹1,200 left. How much did he have?
He is left with 25% = 1200 ⇒ 100% = 1200 × 4 = ₹4,800.

✏️ Practice — try these, take hints as needed

1. A number reduced by 40% becomes 90. The number?
N × 0.60 = 90.
Divide, don’t add.
90/0.6.
150
2. After 15% increase a salary is ₹46,000. Original?
×1.15 = 46000.
46000/1.15.
Reciprocal of 1.15.
₹40,000
3. A bill with 18% GST is ₹1,180. Pre-GST amount?
×1.18.
1180/1.18.
= 1000.
₹1,000
4. 60% of students passed; 80 failed. Total students?
40% failed = 80.
1% = 2.
100% = ?
200
5. A sum becomes ₹2,205 after two years at 5% simple growth per year on the original. Original?
Total +10% over 2 yrs.
×1.10 = 2205.
2205/1.1.
₹2,005 (≈; exact 2004.55)

📝 Topic test — 8 questions

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