## Simple and compound interest

[latexpage] Simple interest $SI = P*R*T/100$ P= principal amount R = rate/unit T = time/year month day etc. Compound interest $CI = P(1+\frac{R}{100})^n$ P= principal amount R= rate/unit T= time unit Where rate are difference for different unit or time. Than $C.I = p(1+\frac{R1}{100}) (1+\frac{R2}{100}) (1+\frac{R3}{100}) ……….$ Present worth of Rs x lac in year … Read more

## Percentage

[latexpage] To express $x\%$ as a fraction =$\frac{x}{100}$ Thus, $3\%$ = $\frac{3}{100}$ = $.03,$ $48\%$ = $\frac{48}{100}$ = $0.48$ = $\frac{12}{25}$ To express $\frac{a}{b}$ as a percentage, we have $\frac{a}{b}$ = $\frac{a*100}{b}$ Thus $\frac{1}{4}$ = $\frac{1*4}{100}$ = $\frac{25}{100}$ = 25% if the price of commodity increases by R% than the reduction in consumption so … Read more

## Surd and Indices

[latexpage] Law of indices 1. $a^ma^n = a^{m+n}$ 2. $\frac{a^m}{a^n} =a^{(m-n)}$ 3. ${(a^m )}^n = a^{mn}$ 4. ${(ab)}^n = a^n* b^n$ 5. $(\frac{a}{b})^n = \frac{a^n}{b^n}$ 6. $a^0 = 1$ laws of surds 1. $\sqrt[n]{a}= a^{\frac{1}{n}}$ 2. $\sqrt[n]{ab}= \sqrt[n]{a} * \sqrt[n]{b}$ 3. $\sqrt[n]{\frac{a}{b}}= \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ 4. $\sqrt[n]{a}^n = a$ 5. $\sqrt[m]{\sqrt[n]{a}} ={\sqrt[mn]{a}}$ 6. $(\sqrt[n]{a})^m = \sqrt[n]{a^m}$

## Boat and Stream

[latexpage] if the speed of a boat in still water is u km/h & the speed of the streams of v km/h than- speed towards downstream- $(u+v) km/h$ Speed towards up stream- $(u-v) km/h$ if the speed of boat in downstream u km/h and in upstream v km/h than speed in still water-$\frac{1}{2}(u+v) km/h$ rate … Read more

## Time and work

[latexpage] If A can do a piece of work in n days then in 1 day’s work $\frac{1}{n}$ If A’s day’s work is 1/n than A can finish the work in n days. Pipes & cisterns Inlet- a pipe connected with a tank/cistern that fill it is known as an inlet. Outlet- a pipe connected … Read more

## Time and Distance

[latexpage] $speed = \frac{distance}{time}$ $X km/hour = x * \frac{1000 metres}{60×60 second} = x*\frac{5}{18} m/sec$ If the ratio of the speed of A & B is a:b then the ratio of time taken by them to cover the same distance is $\frac{1}{a} :\frac{1}{b} = b:a$ “The time taken for covering a certain distance is increasingly … Read more

## Partnership

Partnership When two or more than two persons are a business jointly they are called partners & the deal is known as partnership. Ratio of division of gain. When investments of all the partner are for the same time the gain or loss is distributed among the partners in the ratio of their investment A’s … Read more

## Ratio and Proportion

[latexpage] Ratio – the ratio of two quantity a & b in the same unit is the fraction $\frac{a}{b}$ and we write it a:b In a ratio a:b we call a as the first term or antecedent and b the second term or consequent. Rule– the multiplication or division of each term of a ratio … Read more