Result 1: If A is P% more/less than B, then B is {100P/(100+P)}% less/more than A.

Let us say A is P% more than B
Therefore, we can say:
A = {(100 + P)/100}B
Now, to calculate by what percentage is B is less than A, we need to make the following calculation:
{(A-B)/A} x 100 Now, let us take up the reverse case.
Let say A is P% less than B
Therefore, we can say:
A = (100 – P/100)B
Now, to calculate by what percentage is B is more than A, we need to make the following calculation: Combining the two above, we arrive at our main result.

Result 2:
If the value of an item goes up/down by P%, the percentage reduction/increment that needs to be now made to bring it back to the original point is {100P/(100+P)}%

Result 3: If the price of an item goes up/down by P %, then the quantity consumed should be reduced/increased by{100P/(100+P)}%   so that the total expenditure remains the same.

Derivation for the result:
Expenditure on any quantity = price per piece × total consumed quantity
{For example, if a pen is of Rs. 5 and we have bought 10 such pens, the total expenditure is = 5 × 10 = Rs. 50}
Let P be the original price per time.
Let Q be the quantity consumed.
Original Expenditure= P × Q  ….  (1)
Let say price is increased by R%.
This means that the quantity has to be decreased in order to maintain expenditure constant.
Let’s assume the consumption is decreased by y%.
New Expenditure , E = P{(100+R)/100}Q{(100-y)/100} ………2
Since the original expenditure and the new expenditure are the same, we arrive at the following equation: Remember, each of these results effectively uses the basic concept of percentage and is a derivative of the same.

Example: If A’s income is 60% less than that of B’s, then B’s income is what percent more than that of A? ### Percentages: The Complete Lesson

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