PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoBasic Concepts:
1. To express \(x\) as a percentage of \(y\); percentage \(=\)
2. If \(x\)\(\%\) of a quantity is \(y\), then the whole quantity \(=\)
Fundamental Formulae:
1. Increase/Decrease in quantity:
(i) If quantity increases by \(R\%\), then [Where \(R\) denotes the rate of change in percentage]
New quantity \(=\) Original quantity \(+\) Increases in the quantity
\(=\) Original quantity \(+\) \(R\)\(\%\) of Original quantity
\(=\) Original quantity \(+\) of Original quantity
\(=\) \(\times\) Original quantity
New quantity \(=\) \(\times\) Original quantity.
(ii) Similarly, if quantity decreases by \(R\ \)\(\%\), then, the new quantity \(=\) \(×\) \(\text{Original quantity}\)
2. Population:
(i) If a population of a city increases by \(R\ \)\(\%\) per annum, then the population after '\(n\)' years \(=\) of the original population.
Population after '\(n\)' years \(=\) \(×\) \(\text{Original quantity}\)
(ii) Population '\(n\)' years ago \(=\) \(\frac{\text{original population}}{(1 + \frac{R}{100})^n}\)
(iii) If the population is increased from \(X\) to \(Y\), then the percentage of increase is: \(=\) \((Y - X)\) \(×100\)
3. Rate is more/less than another:
(i) If a number \(x\) is \(R\)\(\%\) more than \(y\), then \(y\) is less than \(x\) by
(ii) If a number \(x\) is \(R\)\(\%\) less than \(y\), then \(y\) is more than \(x\) by
4. Prices of a commodity Increase/Decrease by \(R\%\):
(i) If the price of a commodity increase by \(R\%\), then there is a reduction in consumption, so as not to increase the expenditure. .
(ii) If the price of a commodity decreases by \(R\%\), then increases in consumption, so as not to increase the expenditure. .
If a quantity is increased or decreases by \(x\%\) and another quantity is increased or decreased by \(y\%\), the percent \(\%\) change on the product of both the quantity is given by require \(\%\) change \(=\) .
Note: For increasing use (\(+\))ve sign and for decreasing use (\(-\))ve sign.
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