I came across the following shortcut formulae while going through a text book:
For questions of the type: If the price of a commodity increases by R%, find the % decrease in the consumption given that the expenditure remains same
One can directly find the value by applying: Decrease = 100R/(100 + R)
e.g. If the price of potato is increased by 20%, by how much should the consumption be decreased so as to have no change in the expenditure. Decrease = 100*20/(100 + 20) = 50/3 = 16.67%
Can someone please help me know why the above shortcut formulae works for such type of problems?
Thanks in advance!