i)Addition of Single   Column Method 1)Rule : We know that addition are very easy method. All student know about Addition but they don't know how to solve Addition in less time . At  first we read 5, 7, 12 instead of 5 + 7 = 12 it is take less time . Example : a) 5 + 7 = 12 -------> 5,7,12 b) 18+18 = 36------>18,18,36 c) 12+18 = 30------>12,18,30 d) 10+11 = 21------>10,11,21 2) Rule : For time saving every tens place use * and we add ones place to next number . Example :     7*     5     6*     4     3*     4     8*     5 +  2   -------    44 ------- ii) Addition of Double Column Method For fast addition we add tens and after that we add ones . Example :     56     31     33     55     61 +  32 -------   268      Explain : we start addition from downside  32+60=92+1=93 93+50=143+5=148 148+30=178+3=181 181+30=211+1=212 212+50=262+6=268 iii) Addition of Double Column Method Horizontally Example : 44444   4444     444  +   44         4 --------- 49380 -------- iv) Addition

FORMULA (Problem on Time, Distance & Speed ) i) `Time=(Distance)/(speed)` ii) Distance = Speed X Time                       Distance  iii) Speed = ---------------                        Time                                        5 iv) `x km/hr` = x X ---- m/sec                                        18                              18 v) y m/sec = y X----- km/hr                              5 vi) If a certain distance is covered at x km/hr and the same distance is covered at y km/hr , then the average speed during whole journey = 2xy/(x+y) km/hr. vii) If a man changes his speed in the ratio m:n, then the ratio of times takes becomes n:m. Example on Time and Distance : 1) Express 63 km/hr into metres/sec . Solution :                                 5 63 km/hr = 63 X -------m/sec = 17.5 m/sec.                               18  2) Colambus travels distances of 2500 km , 1200 km and 500 km at the rate of 500 km/hr, 400 km/hr and 250 km/hr respectively. Find the average speed . Solution

Definitions i)Cost Price : The price at which an article /thing is bought is called its Cost Price, it is denoted by C.P. ii) Selling Price : The price at which an article/thing is sold is called its Selling Price, it is denoted by S.P. iii) Profit : When selling price is an article/thing greater than cost price hence Profit . S.P. > C.P. hence Profit . iv) Loss : When cost price is an article/thing greater than Selling Price hence Loss . C.P. > S.P. hence Loss . Note :- Always count profit or loss on Cast Price . v) Marked Price : The price at which mark on an article/thing is called Marked Price .  vi) If an article is sold at a gain of 27% , then S.P. = 127% of C.P.  vii) If an article is sold at a loss of 18% , then S.P. = ( 100 - 18 )% of C.P. = 82% of C.P. Important Formula i) C.P. = S.P. - Profit ii) C.P. = S.P. + Loss iii) Profit = S.P. - C.P iv) Loss = C.P. - S.P.                          Profit X 100 v) Profit %  = ------------------                                   C.

Compound Interest : The amount after first unit of time becomes the principal for second unit of time the amount after second unit of time becomes the principal for third unit of time and so on . After a specified period , the difference between the amount and the principal is called Compound Interest abbreviated as C.I. Sometime C.I. fix up a certain unit of time, say yearly or half yearly or quarterly to settle the previous account . Formula : Let Principal  = P,       Time        =  n,       Rate         =  R% per annum . 1) When Interest is compounded Annually :        Amount = P [ 1 + R/ 100 ]^n 2) When Interest is compounded Half - yearly :        Amount = P [ 1 +( R/2 )/100]^2n 3) When Interest is Compounded Quarterly :        Amount = p [ 1 +( R/4 )/100 ]^4n 4) When Time is Fraction of year :                                                                       3    Le the time be a fraction of a year, say 2------ years                                                           

Simple Interest 1)Principal or Sum : The money borrowed from any bank or any other person is called Principal or Sum. The principal is denoted by P. 2)Time : The money borrowed from any bank of any other person for a fixed period is called Time. Time is denoted by t. 3)Rate : The money borrowed from any bank or any other person for a fixed period and fixed % is called a Rate. Rate is denoted by r. 4) Interest : Extra money paid for using others' money is called Interest. 5)Simple Interest : If the interest is on a certain sum for a certain period and fixed rate it is called Simple Interest. Simple Interest is denoted by SI. 6)Amount : The sum of principal and interest is called Amount. It is denoted by A. Formula Let Principal  = P        Rate         = R%        Time        = T       Then                 P X R X T 1)SI      =  -----------------                   100                 SI X 100 2)P       =    -------------                    R X T                    SI X 100 3)R     =

1) Rule : If one person out and another person come in any group and average age is increase of group then age of another person = age of person out + number of person in group  X increase average age . E xample :  Average age increase by four years of  8 persons group when one person come at place of 30 years old person .What was the age of new person . Sol. Age of new person = age of person out + number of person in group X increase average age                                =        30        +         8      X    4                                      =         62 years 2) Rule : If one person out and another person come in any group and average age is decrease of group then age of another person = age of person out + number of person in group  X decrease average age . Example : Average age decrease by 1/9 years of  45 persons group when one person come at place of 60 years old person .What was the age of new person . Sol. Age of new person = age of person out - number of person in