Percentage

• Percent of a percent:

20% of 30% = 20/100 * 30/100 = 6%

• If A’s salary is r% more or less than B’s salary then B’s salary is 100r/(100 r) % less or more than A

Suppose A’s salary is 20% more than B then B’s salary is 100*20/(120) % = 16.66% less than A

In fact in any relationship where A * B = const. if A changes by r% B changes by 100r/(100 r) % or is you are into factors n/d ⇒ n/(d n).

Speed * time = distance is an ideal example of this. If speed increases by 10% , time decreases by 9.09%.

This is also answer to the question what %  change will offset a % change.

• Next we will move on to successive % changes:

• The next important concept is indexing:

Suppose a company’s sale for 2 consecutive years is 400 and 450 respectively. Then usually the first year’s value 400 is taken as 100 and the relative values of the consecutive years are taken there of.

So 400 ⇒ 100, so 450 ⇒ 450/400 * 100 = 112.5.

• % point change is the difference between two % values.

• S.I:

S.I = [P * r * n]/100

Amount = [1 + r*n/100]*P

Instalment = [x + (x+ (x*r*1)/100) + (x+ (x*r*2)/100) + ...]

• C.I:

Amount = [1 + r/100]^n *P

• Number of years taken for an amount to double under r% C.I is approximately given by: 72/r years.
• CIn - SIn = Pr/100 [(1+r/100)n-1]
• Margin = Profit as % of SP, all other terms are very common.

• Par Value: Value of the share to the company.
• Market value: Value at which the shares are traded at the market.
• Dividend: Profit given to investors.

Mind Map: