You might have seen so many problems especially in ratios which you were able to solve but in more time and not able to reduce the time anymore. increase decrease concept has a lot to do with them.
1/n increase => 1/(n-1) decrease
Any dependent variables in an equation, assume an equation a*b=c.
If you increase 20% in a, it leads to 20% increase in c [when b is constant]
If you increase 20% in b, it leads to 20% increase in c [when a is constant]
This is a simple application which most of us already know from years.
Ever observed this problem, when you increase a certain quantity by 20% and decrease the same by 20% again result in loss and at the same time if you decrease a certain quantity by 20% and increase the same by 20%, it results in the loss. it holds same for any % increase or decrease. but why?
consider a 100 and increase it by 20% => 100+20 = 120
now decrease 20% from it => 120 - 24 (which is 20% of 100 and 20% of the increased 20) so it result in loss.
consider a 100 and decrease it by 20% => 100-20 = 80
now increase 20% from it => 80+16 = 96. so it results in the loss.
so we can draw one conclusion: "If a quantity is increased by x% and decreased by x% (OR) vice-versa (regardless of the order of increase or decrease) results in loss of the same amount"
You have increased a quantity by x%, now by what % you should decrease it to get the same amount?
If you raise 100 by 25% (1/4) it becomes 125, now you need to decrease 20% (1/5) to get back 100.
.............similarly, try with different values of increase (1/2, 1/3,.........1/9)
You can realize a pattern.
conclusion: " (1/n) increase in a quantity + (1/(n+1)) decrease it it results in no change)
so 1/n increase => 1/n+1 decrease
so 1/n+1 decrease => 1/n increase
when you get problems in which you can figure out an equation like "AB =C" and need to operate on any 2 variables, you can apply this concept easily.
Eg. If apples are bought at the rate of 30 for a rupee, how many apples must be sold for a Rupee so as to gain 20%?
here we can interpret a direct relation, Cost = (some term) quantity.
To get 20% profit we need to increase the cost by 20% (1/5) but the cost is same 1 rupee, now In order to balance, 1/5 increase => 1/6 decrease.
[ as we need profit, we don't change the cost and decrease quantity]
so decrease 1/6 in quantity.
= 30 - 1/6(30) = 25.