KBAT Problems
KBAT Problem: Working Backwards from a Percentage
A KBAT problem where you know the result after a percentage change and must find the original, the classic reverse-percentage trap.
The result is not the base
If a price after a 20% increase is RM120, the original is not 120 minus 20%, it is 120 divided by 1.2. The KBAT insight is that the percentage was taken on the original, not the new figure, so you divide to reverse it.
Understand the problem
An original reverse-percentage problem. After a 15% discount, a jacket costs RM204, and you must find the original price.
The trap is treating RM204 as the base and adding 15% back. RM204 is not the original, it is 85% of it, so the original is found by undoing the discount, not by applying it again.
Plan and solve
- A 15% discount leaves 100% − 15% = 85% of the original price.
- So 85% of the original = RM204, i.e. 0.85 × original = 204.
- Original = 204 ÷ 0.85 = RM240.
- The discount is worth 15% × 240 = RM36, and 240 − 36 = 204 ✓.
Check and a variant
Check forward: RM240 with 15% off is 240 × 0.85 = RM204, the given price, so RM240 is correct, while the trap answer 204 × 1.15 = RM234.60 does not check out. A twist in the other direction: a bill is RM212 after 6% service tax is added; the pre-tax amount is 212 ÷ 1.06 = RM200, because RM212 represents 106% of the original.
Whether the change is up or down, divide by the multiplier it created.
Frequently asked questions
Why divide instead of adding the percentage back?
Because the figure you are given is a percentage of the original, not the original itself. After a 15% cut, RM204 is 85% of the starting price, so you recover the whole by dividing by 0.85.
Adding 15% to RM204 works on the wrong base and gives RM234.60, which is close but wrong.
How do I find the right multiplier?
Decide what percentage of the original the given amount represents. A 15% discount leaves 85%, so the multiplier is 0.85; a 6% tax added makes 106%, so it is 1.06.
Then the original equals the given amount divided by that multiplier. Naming the multiplier correctly is the whole battle in reverse-percentage questions.
How can I be sure my original is right?
Apply the change forward and see if you land back on the given figure. If a 15% discount on your answer returns exactly RM204, it is correct.
This forward check costs seconds and catches the classic mistake of multiplying when you should divide, or using the after-price as the base.