Here you are given the value after a change and must rewind to the original. The number in front of you is NOT the base, so never take a percentage of it.
To undo a change, divide
A rise of p% multiplies the original by (1+100p); a fall of p% multiplies by (1−100p). So to get back, divide by that factor — never subtract.
• After +25% a number is 375. Read it as 125% (5 parts): 1 part = 75, original = 4 parts = 300.
• After −15% a salary is ₹17,000 = 85%: 1% = 200, original = ₹20,000.
Price–quantity at fixed spend: spend = price × quantity. If price rises p%, consumption must fall by 100+pp×100 %. A 25% rise needs a 20% cut, not 25%.
🔁Successive % ChangeDivide to undo
final value
change % applied (− for drop)
A +20% change multiplies the original by (1 + 20/100) = 1.2
To rewind, DIVIDE by the factor:
540 ÷ 1.2 = 450
Check forward: 450 × 1.2 = 540 ✓
⚠️ Never subtract the % back: 540 − 20% = 432 ✗ — that 20% sits on the wrong base. −10% then +10% does NOT undo: 100 → 90 → 99, not 100. Undoing is division, not the opposite %.
Original = 450
After a 20% rise a number is 600 (= 120%). The original is 600 ÷ 1.2 = .
📝Practice Questions
Q1After a 25% rise a number is 500. The original was:
Q2After a 20% discount a price is ₹640. The marked price was:
Q3If sugar price rises 25%, consumption must fall by ___ to keep spend fixed:
📚
Real exam questions — Reverse % & Net Change
3 question types · 9 solved examples from real SSC papers
You are given the value AFTER the change and must rewind to the original — divide by the multiplier, never subtract.
How to solve this type
The final value is NOT the base, so never take the percentage of the number you are handed. A rise of p% multiplies the original by (1+100p), so to undo it you DIVIDE the final by that factor; a fall of p% multiplies by (1−100p), so divide by that. Fastest is the fraction form: +25% means ×45, so original = final ×54; −20% means ×54, so original = final ×45. Read the given number as (100±p)% and scale it back to 100%.
After a 10% increase a quantity becomes 660. The original value was:
A590B600C580D610
After a 15% cut a salary is ₹17,000. The original salary was:
A₹19,000B₹20,000C₹18,500D₹21,000
After a 25% increase a number is 375. The original number was:
