1. To express “anything” as percentage, simply “multiply” it by 100
ex. 3 can be expressed as 300%

2. To remove % sign, divide by 100
ex. 50% means 50 / 100 i.e. 1 / 2

3. Percentage Change (PC):
PC=(New Amt - Old Amt)/(Old Amt) x 10

4. X increased or decreased by a% is given by
(100 / (100+- a) ) X x

5. Two successive changes: If two successive discounts of ‘x%’ & ‘y%’ is done, then these are equivalent to a single change of [x+y+xy/100]%

6. In most of the percentage problems, instead of assuming the unknown as ‘x’ we start with 100 for easy calculations.

Ex. 1: A man’s wages are increased by 10% and then decreased by 10%. What is the total percentage change.
Sol. 1: Total Percentage change=[10-10-(10×10)/100]= -1 %.
i.e. wages are decreased by 1%

Ex. 2: If the price of tea be increased by 20%, find by what percent must a person reduce his consumption so as not to increase his expenditure.
Sol. 2:In this type of question, use direct formula percentage change
It is given by [r/100+-r]x100 where r=percentage change in price. Use ‘+’ for increase in price & ‘-’ for decrease in price.
Percentage change= (20 x 100)/120 = 50/3 %

Ex. 3: Ram gets 30% more salary than Shyam. Then by what percent does Shyam gets less salary than Ram.
Sol. 3: Such pblms can also be solved by %less salary = [r/(100+r)] x 100%
Hence Shyam gets 30 x 100 / 130= 23.07 % less salary.

[NOTE : Use r x 100/(100 - r) for finding % more salary].

Ex. 4: The population of a town is 30,000. If the number of males was increased by 4% and the females by 7%, the population would become 31,380. Find the number of males and females in the town.
Sol. 4: This question can be solved using simultaneous equation, but we apply a different approach. Let us assume the whole population increases by 4% (i.e. both males and females). The new population would increase by (30,000 x 4)/100 =1200. But actual increment is 31,380-30,000=1380. Where does this extra 180 come from?
Yes, 3% females = 180
So, Females=6000 & males=24,000.

Ex. 5: A reduction of 10% in the price of sugar enables me to obtain 25 kg more for Rs. 225. What is the reduced price per kg and also find the original price per kg.
Sol. 5: A simple solution is to think in the following steps
step 1: the extra 25 kg is obtained because of 10% reduction in price i.e. 10% of 225 = Rs. 22.50
step 2: Reduced price per kg = (22.50)/25
= Rs 0.90/kg
step 3: 10% reduction in price means you pay 90% of the original price.
=> 90% of original price =.90/kg
=> original price=Rs. 1/kg.

[NOTE: Remember by this method we obtain the reduced price first. So even if in the question the original price is asked, you have to find the reduced price first].