Profit or Loss Justification

Question

What is the justification of the following two sentences:

1.If an article is sold at a gain of 35% then its selling price is 135% of Cost price.

2. If an article is sold at a loss of 35% then its selling price is 65% of cost price.

Answer 1

I am not sure what justification you want here but If ideally you consider all the other expenses to be null(i. e transporting, maintaining, etc.) or consider the cost price to include all the other expenses only then are the above statements justified...

Answer 2

Remember that the base value is $1$ times of its original value, which translates to $100$% of the original value. We can say this because by definition, $100$ lots of $1$ percent make up a whole part (equal to $1$).

Therefore, a percentage gain of $35$% results in $100$% + $35$% = $135$%,
and a percentage loss of $35$% results in $100$% - $35$% = $65$%.