Percentage means for every hundred. The symbol % must be replaced by a fraction 1/100. A percentage must be expressed as a fraction or a decimal.this concept is developed to make the comparison fractions easier by equalising the denominators of all fractions to hundred.
for example, 7/11 as percentage is represented as 7/11 = 63.63%
Percentages can also be re[presented as decimal fractions. in such a case it is effectively equivalent to the proportion of the original quantity. for example, 20% is same as 20/100, i.e., 0.2
Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100 and conversely, any decimal fraction can be converted to percentage by multiplying it by 100.
Percentage Increase or Decrease of a quantity is the ratio expressed in percentage of the actual Increase or Decrease of the quantity to the original amount of the quantity, i.e.,
Actual increase = 242 -225 = 17 MT
Percentage increase = ( Quantity increase from 1993 to 1994/Actual production of rice in 1993 )*100
= 17/225 * 100 = 7 5/9%
Ratio of any two quantities can be expressed as percentage. for example, if the ratio of A and B is 3:2, we can say the ratio of A : Bis 60% : 40%.
Whenever there is any percentage increase or decrease on a quantity, we can directly calculate the new value of the quantity instead of calculating the actual increase/decrease and then adding to/ subtracting from the original quantity. for example, if the increase on a value of 350 is 15%, the new quantity is 1.15 * 350 = 402.5 (where 1.15 = 1+0.15, 0.15 being the decimal equivalent of 15% )
If the production in 1994 is given as 400 MT and the increase from 1993 to 1994 is given to be 25%, then the production in 1993 will be equal to 400/1.25 = 320 MT. similarly, if there is a decrease of 12% on a quantity of 225, then the new quantity will be equal to 225*0.88 (where 0.88 = 1-0.12, 0.12 being the decimal equivalent of 12% )
On the basis of percentage increase, we can write down how many times the old value gives the new value. for example, if the percentage increase is 100%, then we can conclude that the new value is 2 times the old value. if the percentage increase is 300%, the new value is 4 times the old value. if the percentage increase is 450%, then the new value is 5.5 times the old value. in general, if the percentage increase is p%, then the new value is (p/100 + 1) times the old value.
conversely, if we know how many time the old value gives the new value, we can find out the new percentage increase in the old value to get the new value. for example, if the new value is 3 times the old value, the percentage increase in the old value to get the new value is 200%. if the new value is 4.25vtimes the old value, then the percentage is 325%. in general, if the value is k times the old value, then the percentage is (k-1)*100.
Examples
1. The number of tourists visiting a country increased by 80% from 1990 to 1991. from 1991 to 1992, there was a 50% increase. find the percentage increase in the number of tourists visiting the country from 1990 to 1992.
Solution: Let the number of tourists visiting the country in 1990 be 100. As the number of visitors increased by 80% from 1990 to 1991, the number of visitors increased by 80% of 100 i.e., 80. Hence, the number of visitors will be 180 in 1991. then, there was 50% increase from 1991 to 1992. this country will be 180 + 90 (50% of 180) = 270. so the number of tourists to the country went up from 100 to 270 in 1992, an increase of 170 from the initial number of tourists of 100. hence the percentage increase = ( increase/initial )*100 = 170/100*100 = 170%.
=>In general, if there are successive increases of p%, q% and r% in three stages, the effective percentage increase is {(100+P/100)(100+Q/100)(100+R/100) - 1}*100.
If one or more of p, q and r decrease percentage figures and not increase percentage, then it will be taken as a negative, then it will be taken as a negative figure and not as a positive figure.similarly, if the resultant figure is negative, it means it is a net decrease.the same can be extended to any number of successive increase or decrease percentages.
2. The ratio of salaries of mehata and dixit is 20:21, by what percentage is 20:21. By what percentage is dixit's salary greater than that of mehata ?
Solution: The given ratio is 20:21. This means, the salary of dixit is 21 parts when the salary of mehata is 20 parts. Percentage by which Dixit's salary is greater than Mehta's
= (21-20)/20*100 = 5%.
3. If the price of an item goes up by 10%, by what percentage should the new price be reduced to bring it down to the original price ?
Solution : Let the original price be 100. now it becomes 110, due to 10% increase. now, to bring this down to the original price, we have to effect a reduction of 10 from 110. hence percentage reduction 10/110*100 = 9.09%
=> In general, if the value of an item goes down by X%, the percentage increment to be now made it bring it back to the original level is = 100X / (100 - X). if the value of an item goes up by X%, the percentage reduction to be now made it bring it back to the original level is = 100X / (100 + X).
Percentage Points
the concept of "percentage points" is important in the usage of percentages. percentage points is the difference of two percentage figures.
Let us understand this with an example. suppose that rice forms 20% of total food grain production in year the I and 30% of total food grain production in year II. If we asked to find out the percentage increase in the production of rice, calculating percentage increase from 20 to 30 as 30-20/20*100 and saying it is 50% increase is NOT correct. with the available data, we cannot find out the percentage increase in the production of rice from year I to II. wee can only say that the production of rice as a percentage of total food grain production went up by Production Points.
We can see by taking the following figures that the percentage increase in rice production need not be 50%. In year I rice -1000, total food grains - 5000, rice as percentage of total food grains - 20%. similarly, In year I rice -960, total food grains - 3200, rice as percentage of total food grains - 30%.
Here, while the rice is 20% of the total food grains in year I and 30% of total food grains in year II, we find the actual production of rice has not even increased - it decreased from 1000 in year I to 980 in year II.
for example, 7/11 as percentage is represented as 7/11 = 63.63%
Percentages can also be re[presented as decimal fractions. in such a case it is effectively equivalent to the proportion of the original quantity. for example, 20% is same as 20/100, i.e., 0.2
Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100 and conversely, any decimal fraction can be converted to percentage by multiplying it by 100.
Percentage Increase or Decrease of a quantity is the ratio expressed in percentage of the actual Increase or Decrease of the quantity to the original amount of the quantity, i.e.,
- Percentage Increase = ( Actual Increase/Original quantity )*100
- Percentage Decrease = ( Actual Decrease/Original quantity )*100
Actual increase = 242 -225 = 17 MT
Percentage increase = ( Quantity increase from 1993 to 1994/Actual production of rice in 1993 )*100
= 17/225 * 100 = 7 5/9%
Ratio of any two quantities can be expressed as percentage. for example, if the ratio of A and B is 3:2, we can say the ratio of A : Bis 60% : 40%.
Whenever there is any percentage increase or decrease on a quantity, we can directly calculate the new value of the quantity instead of calculating the actual increase/decrease and then adding to/ subtracting from the original quantity. for example, if the increase on a value of 350 is 15%, the new quantity is 1.15 * 350 = 402.5 (where 1.15 = 1+0.15, 0.15 being the decimal equivalent of 15% )
If the production in 1994 is given as 400 MT and the increase from 1993 to 1994 is given to be 25%, then the production in 1993 will be equal to 400/1.25 = 320 MT. similarly, if there is a decrease of 12% on a quantity of 225, then the new quantity will be equal to 225*0.88 (where 0.88 = 1-0.12, 0.12 being the decimal equivalent of 12% )
On the basis of percentage increase, we can write down how many times the old value gives the new value. for example, if the percentage increase is 100%, then we can conclude that the new value is 2 times the old value. if the percentage increase is 300%, the new value is 4 times the old value. if the percentage increase is 450%, then the new value is 5.5 times the old value. in general, if the percentage increase is p%, then the new value is (p/100 + 1) times the old value.
conversely, if we know how many time the old value gives the new value, we can find out the new percentage increase in the old value to get the new value. for example, if the new value is 3 times the old value, the percentage increase in the old value to get the new value is 200%. if the new value is 4.25vtimes the old value, then the percentage is 325%. in general, if the value is k times the old value, then the percentage is (k-1)*100.
Examples
1. The number of tourists visiting a country increased by 80% from 1990 to 1991. from 1991 to 1992, there was a 50% increase. find the percentage increase in the number of tourists visiting the country from 1990 to 1992.
Solution: Let the number of tourists visiting the country in 1990 be 100. As the number of visitors increased by 80% from 1990 to 1991, the number of visitors increased by 80% of 100 i.e., 80. Hence, the number of visitors will be 180 in 1991. then, there was 50% increase from 1991 to 1992. this country will be 180 + 90 (50% of 180) = 270. so the number of tourists to the country went up from 100 to 270 in 1992, an increase of 170 from the initial number of tourists of 100. hence the percentage increase = ( increase/initial )*100 = 170/100*100 = 170%.
=>In general, if there are successive increases of p%, q% and r% in three stages, the effective percentage increase is {(100+P/100)(100+Q/100)(100+R/100) - 1}*100.
If one or more of p, q and r decrease percentage figures and not increase percentage, then it will be taken as a negative, then it will be taken as a negative figure and not as a positive figure.similarly, if the resultant figure is negative, it means it is a net decrease.the same can be extended to any number of successive increase or decrease percentages.
2. The ratio of salaries of mehata and dixit is 20:21, by what percentage is 20:21. By what percentage is dixit's salary greater than that of mehata ?
Solution: The given ratio is 20:21. This means, the salary of dixit is 21 parts when the salary of mehata is 20 parts. Percentage by which Dixit's salary is greater than Mehta's
= (21-20)/20*100 = 5%.
3. If the price of an item goes up by 10%, by what percentage should the new price be reduced to bring it down to the original price ?
Solution : Let the original price be 100. now it becomes 110, due to 10% increase. now, to bring this down to the original price, we have to effect a reduction of 10 from 110. hence percentage reduction 10/110*100 = 9.09%
=> In general, if the value of an item goes down by X%, the percentage increment to be now made it bring it back to the original level is = 100X / (100 - X). if the value of an item goes up by X%, the percentage reduction to be now made it bring it back to the original level is = 100X / (100 + X).
Percentage Points
the concept of "percentage points" is important in the usage of percentages. percentage points is the difference of two percentage figures.
Let us understand this with an example. suppose that rice forms 20% of total food grain production in year the I and 30% of total food grain production in year II. If we asked to find out the percentage increase in the production of rice, calculating percentage increase from 20 to 30 as 30-20/20*100 and saying it is 50% increase is NOT correct. with the available data, we cannot find out the percentage increase in the production of rice from year I to II. wee can only say that the production of rice as a percentage of total food grain production went up by Production Points.
We can see by taking the following figures that the percentage increase in rice production need not be 50%. In year I rice -1000, total food grains - 5000, rice as percentage of total food grains - 20%. similarly, In year I rice -960, total food grains - 3200, rice as percentage of total food grains - 30%.
Here, while the rice is 20% of the total food grains in year I and 30% of total food grains in year II, we find the actual production of rice has not even increased - it decreased from 1000 in year I to 980 in year II.
good tricks
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