How do you find the original value in a percentage question?

Let's assume (oh my!) we can use the "multiplier method" for this.

Q: After an amount is increased by 20%, the answer is 90.

What is the amount before the increase?

A: Let's use Bm = A

Where B is the amount before the increase, m is the multiplier and A is the amount after the increase - so:

B(1.20) = 90

B = 90/1.20 = 75

So, the amount before the increase is 75.

Another way to find the original amount is as follows:

The original amount is 100%

The new amount is either 100% + increase% or 100% - decrease%

To get back to the original divide by this % number and multiply by 100.

Example: Sale price is £180 after a discount of 10%

New amount = £180 = 100% - 10% = 90%

£180 = 90%

Divide by 90 to get 1%

£2 = 1%

Multiply by 100 to get 100%

£200 = 100% = original amount

You can't find 10% of £180 and add it on to get back to the original amount because the 10% that was subtracted was 10% of the original amount which was larger and is unknown at the start of the question.