Percentages are special types of fractions in which the denominator is always hundred.
e.g.
It is written as 10% or its simplified form is
Percentage Increase/Decrease:
If the price of a commodity increases by a%, then the reduction in consumption so as not to increase the expenditure is:
If the price of a commodity decreases by a%, then the increase in consumption so as not to decrease the expenditure is:
Results on Population:
Populations after n year = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEjE_DWq0XqVWGF_wrfbt5GOTAvGKZDKRlN7UfEOoDR8JSNbMVa36W81ONk2Ag8eqkWURPXMHUGsN465jwpZqNyTFZtbtbor5AHLKeIHb8tpNA0Dcpt9GWuiFBrvNn4F9zJLW5bZ45BBBzyaYdi9iN0G2oSFDfwyaD3Nn8Z4-_GnvKxBUFG5oVeFFevYFVs=)
Populations before n years = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEj_8CIdjdJfI-Rr5dN5RQ51Yn75LIUPx3fx8JjigdzRhPcE0wDnk6AoU0l6-R1TDDhZZW7nQpayMuxWAqR9QmGukOQUnSaPmeANQNAaTiPu1FdTNUNznCiJmQ-JPjP2DtKvLqHyPFJZ_dIsicsnE1AT6h3se1_QoIPPEj6Gzr1IunTZHTNGmEV6DUW7Jlk=)
If the value of a number is first increased by a% and later decreased by a%. then the net effect is always decreased which is equal to a% of a and is written is ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEjWzXmdZOFxoPJaWwyh68OTGnNKBYqSE-AxLWf51_Y97ZoRIV4XjpSVr3L_FA28Peii4eccAZESsLRnDw_NiMkWPfKy5mpoiupU5a4svlzq8Lw2MJySY4Pw_q7BGMwptF1jj_ZM0omFekcwuZZgKjjj7u-YdbbEAHv6LgghbZLFIaem1n7IXb144zBskN0=)
SOME IMPORTANT FRACTION VALUES :-
EX: A's income is 10% more than B's income. How much per cent is B's income less than A's income?
Sol: Let B's Income = Rs. 100
A's income =
= Rs. 110
Required percentage =
%
= 9
%
Ex: In an examination, 35% is passing marks one candidate obtain 135 marks and failed by 40 marks then find the maximum marks?
Sol: 35% = 135 + 40
100% = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEiLyYHJBPqXbs7h_8ycl35gNoh37hzKcBFsuu7Fl-mX-8F-XY5CJwRBKWenLUekbsOdPFWr0q3tSJKoLxqNm-tAdtUR9omwgo6SdpsHbULErw3tpOp_kH9EyoXyQt9tgKmP_hNa-SvEXOXWR-ko0BjaTnZu_yhpU_PBqB640onvXCIW2BLmk8luFY6r2AQ=)
= 500
Ex: Rohit obtained 480 marks out of 600 and Mohit obtained 560 marks out of 800. Whose performance is better and how much %?
Sol:
Rohit got =
x 100 = 80 %
Mohit got =
x 100 = 70 %
Rohit performance is better.
% better =
x 100 = 14
%
Ex: In an election between two candidates, 65 votes were declared invalid one candidate gets 52% votes and win by 98 votes.Find the total number of votes?
Winner 52% Looser 48%
4% = 98
100% = 2450
Valid vote = 2450
Total vote = 2450 +65 = 2515
Ex: The length and breadth of the rectangle are increased by 30% and 20% respectively, so find the net % change in its area?
Sol:
Net % change = x + y + ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEiiKrnl91z7Du2I25MOW22DUO2Tko6Whpqhja1TJjbWLrcL3mOQ0sX6GCr6E0VZAgrWLJQRDDQkGhVg7fxCdBiFzv1XIqlkgVqpFsECK429vGveNgEjzQwrbZ95ugRr4l11qyFjrqOGbviALwr6bVmOpb23uGcpF43ZWD6IQ0lBS0vGYICRu2zymUYx4jA=)
= 30 + 20 + ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEjrmyGU50ER4CUUIXqZlHy6Q4FHVW7yIfu-5Q0b1i43Qs-OTSfpUFNqX2Xx0NW-RjJX6d9oT-t0eGiug-4h6OaKklwZKiYX_sylil27y_O_c8zpbgkh_QwBCYoBNpjpqd1CJZ-DZ7suFiZZlmHIArEwh-3h4TONjdt0tBM44FK9r6CIMBezCC1GhVnd0Ew=)
= 56%
Ex: A number is mistakenly divided by 10 instead of being multiplied by 10.What is the percentage error in the result?
Sol:
Let the number is 10.
Actual result = 10 x 10 = 100
Wrong result =
= 1
% change =
x 100 = 99%
Ex: The numerator of a fraction is increased by 400% and the denominator is increased by 500%, so the resultant fraction is 15/22. Find the original fraction?
Sol:
Original Fraction
=
Original Fraction = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEgQKc5Ij0sksp-luQqKh84zZd09al6AHs2NCALnFihtlx5uKsG9efbiQCignNQHWDgLnbVIv3kLW5vIhC4uq18LangmcsubLhSUHjFeujQqfX18YkIOIZCqsm-Wz9k9bMrao3yT5hmxcPKYKhiCTrEa1yL5WdIZ_ZGNo24-WJaMaEFB8lxahCceppEYwzc=)
Ex: A, B and C are three persons. A earned 40% more than B and B earned 20% less than C, so what % more earned A than C.
Sol:
A B C
112 80 100
A more earned than C = 112 – 100 = 12
= 12 %
Ex: Due to reduction of 20% in the price of apples enables a person to purchase 16 apples more for Rs.320, so find the reduced rate of 10 apples?
Sol:
Reduced rate =
= 64
Reduced rate of 1 apple =
= Rs. 4
Reduced rate of 10 apples = 4 x10
= Rs.40
Ex: A mixture of 40 litres of milk and water contains 10% water. How much water should be added, so water may be 20% in the new mixture?
Sol:
40
4 lit.
80% = 36
1% = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEguelPCVFxkEMpG1Ps7lp0e3m4MBC3nTIZR1Nl556AjmS7IHcMomz5t9d951fJBukVyOxDrBTCYcVFTyYE6glmkl6fTGbi0qIzWRxX8r1ymXvym94PdmtSvSEkmmd_tzEhYB_oPnZoiALF25sS11vaFSryz6sVjyERVMUcImw7Oz8zjvAYKOOEA5oLh4Jg=)
20% = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEgxE61Wnlnywt4xTd3GmQrAWfC4hgu6Hq_9H05TAQDTa1ny0EtlCjcEsrxWtqDuOx2a5dFBoFhGQxAok0pVybiGlIuGu-MVrnBUmsoPuNdrrSl6Bw0afXOqIBPeatjHJq9CHYPMsM2svuGBAR0qTvMEV00kDMFrFXa0d0rFpm-iE5QS3tgDiMqgrf8h4Us=)
= 9 Lit.
req. water = 9 – 4
= 5 lit.
Ex: Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg. of fresh fruit ?
Sol:
fruit content in 100 kg. of fresh fruits = 100
= 32 kg.
Since , dry fruits contain 80% fruit content,
80% = 32
1% = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEjakTA-4MhhopCFdcnB9bjHByYy8FWNLF9p9TArAJiiNQ2E6TZZ4VJDNAEXuCdg9pxMfdLLIIj9fW-iQtTmGpfsQidIkyRj-8yrRhLjQbKho6Idlg0CcF3tQkbJ8Xd-hbe6CzOu6DWyllSaovRGAXaial23wXF0XHQgYFpa422AgPVccKzoQQ8Tm2WE4bI=)
100% = ![Important Notes : Percentage Important Notes : Percentage](https://blogger.googleusercontent.com/img/proxy/AVvXsEiMr1ElngfvJaUUissI29FrVf0yISlLC9tzXDzPibVDxlHMVI66eZXvkDvziQkWCnpFKr0rgYAarGj8JBnJi4PD8tNiOPapq-14OwaaWqEdFNLcM6-iskzhEX5TxOtN8sKZqzU96H-GlqkTYaZEqjM-UKC7XfUq_rrk_OCstT1e6KwrrD094N2M6Au3-9c=)
= 40 kg.
Ex: In an examination, 35% of the candidates failed in Mathematics and 38% failed in English. 28% passed in both subjects, then how much percent failed in both the subjects?
Sol: Failed in Maths = 35%
Passed in Maths = 100%
35% = 65%
Failed in English = 38%
Passed in Maths = 100%
38% = 62%
Failed in both subjects = 100% – (37%+28%+34%)
= 1%
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MAHENDRA GURU