Math and Reasoning

Probability Probability is just the chance of happening of an event . In other words , Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence which is expressed as a number between 1 and 0.  e.g.  The probability of a coin toss resulting in head is 1/2. The probability is defined as the chance of happening or not happening of an event. Important terms Related to probability : * Experiment  An action which result in some well-defined outcomes . * Random experiment  A random experiment is an experiment or a process for which the outcomes cannot be predicted with certainity .    Whenever an experiment is conducted a number of times under similar condition where the resultis not certain , then the experiment is called a trial or a random experiment , the outcomes are known as events. e.g. When a die is thrown , it is a trial , getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event. *...

Permutation and Combination permutation and combination are ways for the arrangement or selection of a group of persons/ numbers etc. Permutation is an act of rearrangement all the members of a set into same sequence or order.It is one of the different arrangement of a group of items where order / sequence / way matters whereas combination is a way of selecting members from the group such that the order of selection doesn't matter. Fundamental principle of multiplication  It there are two jobs such that one of them can be completed in m ways and second job can be completed in m ×n ways. e.g. If there are 4 ways in which a person can go from X to Y and 7 ways in which he can go from Y to Z , then possible ways to go from X to Z = 4 ×7 = 28 ways. Fundamental principle of addition If there two jobs such that they can be performed independently in m and n ways respectively , then either of the two jobs performed in (m+n) ways. Permutation By permutation we mean...

Simple and compound Interest Simple Interest:- Basic formulae for calculation of various parameters related to simple interest  are explained as under If P= Principal, R = Rate per cent per annum ,T= Number of years, SI = Simple interest and A = Amount, Then Elementary Formulae on Simple Interest 1.Change of rate of interest and time when interest is calculated for different specified time.    if original rate = R% and time  = T yr , Then    For half-yearly, rate = R/2 % and time = 2T    For quarterly, rate = R/4 % and time = 4T    For quarterly, rate = R/12 % and time =12T 2. When a sum becomes n times of its in T yr at a rate of R% per annum, then RT = (n-1) x 100 3. When the simple interest on a sum at R% per annum in T yr is X/Y of the sum, then for R = T       T = R = √ [(x/y) x 100 ] 4. When two equal sum are deposited for T 1 and T 2 at the rate of interest of R 1 % and R ...

Speed Speed is the total distance covered by an object in unit time interval .It is obtained by dividing distance covered by the time to cover the distance. Speed=Distance Travelled /Time taken Also, distance = Speed x Time taken Time Taken = Distance travelled / Speed Here, the unit of speed are km/h,m/s etc. Average Speed Average Speed is the ratio of total distance covered to total time taken to cover the distance. Relative Speed When two object are moving , then you have to take into consideration their relative speed in place pf their individual speeds. Relative speed is the Speed of one object with respect to other. CASE 1:-  x km/h A------→ x m/s B-----→ when two object are moving in the same direction with x km/h and y km/h respectively. Relative speed = (x-y) km/h                           (y-x...

Concept of work and time         It is assumed that , if a problem does a work in n days or a pipe fills a cistern or reservoir in n days in n days , then equal amount of work on each of those days i.e. work done in a day is equal to 1/n,  Also, number of days to complete a work = 1/(work done in one day). →Efficiency is inversely proportional to the time (i.e. number of days/minutes/hours etc.). FUNDAMENTAL FORMULAE        Let M 1 men can complete W 1 work in D 1 days working H 1   h per day and earns a wages  of  ₹ R 1 Similarly , let M 2 men can complete W 2 work in D 2 days working H 2 h per days and earns a wages of ₹ R 2 Then, Efficiency problem:-     If a person A is twice as efficient as B in doing a certain work , then time taken by A is half the time taken by B to complete the work. i.e. the ratio of time taken by A and B to do the same piece of work is 1:2. ...

   Ratio,Proportion,Partnership and Mixture Ratio :-        Ratio compares two or more quantities of same kind with each other by method of division.It is a relation that one quantity bears to another with respect to magnitude or in other words, ratio of two quantities is the number of times of one quantity contains another quantities of same kind.        If a and b are two quantities of the same kind,then a/b known  as the ratio of a and b . It is clear that ,the ratio of two quantities is equivalent to the fraction of one quantities to the other.        Thus , a to b is the ratio (a/b) , written as a:b.          The first term of the ratio is called antecedent while the second term is called consequent.           A ratio remains unchanged . if each term of a ratio are multiplied or divided by the...

Profit,Loss and Discount COST PRICE :-       cost price of an article or a product is the price at which it is purchased  or it is simply the money paid to buy a product.It is abbreviated as CP.       When an article is purchased at some price and some money is spend on its repair or transportation or labour or commission etc. then these expenses are added to the cost price,such expenses are called overhaed expenses and the actual cost price of article will be equal to sum of cost price and overhead expenses. Actual cost price = Cost price + Overhead expenses. Selling Price :-           Selling price of an article or a product is the price at which it is sold or the money obtained after selling the article to other.It is abbreviated as SP. Profit or Gain:-        If the selling price of an article id more than the cost price of the article , then it is said that a...

Order of Magnitude Here is the some solved problem on order of magnitude

Percentage Question and Solution.

Average In This section there Are some question on Average of number and different manipulation on Average like Distance traveling , or timing and many other problem with is help in To Crack IAS and SCC exams......