Logarithms

[latexpage] It is a passive real number other than $a^m = n$ We write $m=log_a x$ $10^3 =1000$4 then we can write $log_{10} 1000 = 3$ $2^{-3} =\frac{1}{8}$ then we can write $log_2 \frac{1}{8} = -3$ Properties of logarithms $log_a (xy) = log_a x +log_a y$ $log_a (\frac{x}{y}) = log_a x – log_a y$ $log_x … Read more

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

Alligation Or Mixture

[latexpage] Alligation- the rate to find the ratio in which two or more ingredients at the given price.must be mixed to produce a mixer of a desired price. Mean price- the cost price of a unit remobilty of the mix are is called mean price. Rule of allegation $\frac{(quantity of cheaper)}{(quantity of deaver)}= \frac{(c.p of … Read more

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 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

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

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

Profit and loss

[latexpage] Cost Price– the price of which an article is purchased is called its cost price(CP) Selling Price– the price at which on article is sold , is called its selling price (SP) Profit or Gain– if SP is greater than CP , the seller is said to have a profit. Loss- if SP is … 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