MATHEMATICS ADDA 786

    PERCENTAGES is very important chapter for all  competitive  exam and everything is included in it like all Problems on percentages,  fractions and percentages, price change,result and population,results on depreciation,comparison of percentages,successive increase and decrease etc. Percentages The Percentage is a fraction whose denominator is always 100. The percentage sign is %. Example -   7% can be converted to a fraction as 7/100 = 0.07   If, we want to calculate P% of Q, then    Percentage Formula:-      P% of Q =  Q× P/100 Qes.  If 30% of x = 60, then find the value of P. Soln .      x × 30/100 = 60 ⇒ x = 60 × 100/30 ⇒ x = 200. Fractions and Percentages To express Y % as a fraction,    Y% = Y/100   As -  30% = 30/100 = 3/10          98% = 98/100 = 49/50 To Express X/Y as a percentage we can say,   X/Y = (X/Y × 100) % ...

PROBLEMS ON AGES is very important chapter for all  competitive  exam and everything is included in it like all Problems on Ages,types of question and some important qes. PROBLEMS ON AGES Problems based on ages in past, present or future of two or more persons and we will find required information by using these given information.   Types of Questions:   Ratio and Sum of ages given * If the ratio of present age of P and Q is x : y and their sum of present age is A         then        P = [ x / (x+y) ]× A        Q = [ x / (x+y) ]× A Qes.  If the ratio of present age of Alok and Khushi is 8 : 5 and their sum of present age is 52 years, find the present age of Alok? Soln.     Let, age of Alok be 8x and age of Khushi be 5x            Then, sum of both ages = 8x + 5x = 13x ⇒ 13x = 52 ⇒ x = 4 years ∴ Age of Alok = 4x = 4 × 4 = 16 years Alternate solutio...

 PARTNERSHIP is very important chapter for all  competitive  exam and everything is included in it like all partnership,profit and capital,mix partnership based on some important qes.  PARTNERSHIP It is based on three points, first we have to use time , 2nd we will use investment and 3rd is profit . Profit directly proportional to  investment  OR Profit ∝ investment   Profit directly proportional to time OR Profit ∝ time Therefore, ratio of profit is directly proportional to the product of investment and time. Profit and Capital Profit (P) ∝  Capital (C)  P₁:P₂ = C₁:C₂ Qes. A, B and C started a business with Rs. 20,000, Rs.24,000 and Rs.30,000 respectively for 2 years and they get Rs.111,000 as profit. Find the B's share in the profit. Soln. Ratio of investment of A,B and C= 20,000 24,000 30,000 = 10 : 12 : 15  The profit of B =  [12 ÷ (10+12+15)]×111000 = 36000 Mix Partnership When the partners are involved for different T...

AVERAGES are very important chapter for all  competitive  exam and everything is included in it like all averages, series, important key, batting ball wicket based on some important qes. AVERAGE  It is defined as the sum of the observations divided by the number of observations. Average = sum of the observations / Number of observations  OR,  Average = sum of Quantity / Number of    Quantity * IN SERIES(AP) : -  Average = (1st Number + Last Number) / 2 If number of terms is Odd Average = Mid. Term Qes. The average age of a hockey team of six players is 25 years. If two more players are included in the team the average becomes 26 years, then the Soln.  Average age of six players is = 25 years => Sum of age of 6 players = 25 x 6 = 150 years => If two players are included in the team, then average age of 8 players = 26 years =>Sum of age of 8 players = 8 x 26 = 208 years => Sum of age of two players (included) = 208-150 = ...

SIMPLIFICATION AND APPROXIMATION  is very important chapter for all  competitive  exam and everything is included in it like all simplication and approximation, simplication,fraction,decimal, surds and indices etc. SIMPLIFICATION AND APPROXIMATION SIMPLIFICATION:  It means reducing the expression in simpler form using various functions. The function used to simplify follows a fixed order known as BODMAS Where, B = Bracket O = of D = Division M = Multiplication  A = Addition S = Subtraction Brackets:  There are three types of brackets:- 1) Round brackets  ()  2) Curly brackets {} 3) Box brackets [] 1st we shall use the bracket () {} and [] . OF means multiplication but it is used before division. then we can use addition and substraction. APPROXIMATION :   It is simplifying(clarify) the mathematical expression to its nearest value but not exactly correct.   when we find out the approximate value, we have to round off the digit...

number system is very important chapter for all  competitive  exam . everything is included in it like all numbers,some special number,divisibility concept,unit digit,divisibility remainder concept,decimal and number of factor,key to remainder concept,lcm and hcf etc. LCM AND HCF Highest Common Factor (H.C.F): -  When a largest(greatest) number divides perfectly two or more numbers it is called hcf. We can find the H.C.F of two or more number by division method and factorization method Formula:  H.C.F of two or more numbers = product of common prime factors of lowest power. Most important key  # 1st number × 2nd number = LCM × HCF #Product of n number = LCM × HCF^n-1  (IF more than two numbers) #HCF of x/a , y/b , z/c = (HCF of x,y,z)/LCM of a,b,c #LCM of x/a , y/b , z/c = (LCM of x,y,z)/HCF of a,b,c Example:  H.C.F (12,288) 12 = 2^2 x 3 and 288 = 2^5 x 3^2  So, H.C.F=2^2 x 3=12 Lowest Common Multiple (L.C.M): - The least number which is divi...

number system is very important chapter for all  competitive  exam . everything is included in it like all numbers,some special number,divisibility concept,unit digit,divisibility remainder concept,decimal and number of factor,key to remainder concept,lcm and hcf etc. UNIT DIGIT Unit digit is used to represent the "ones" place value of any number or product.  Example:- 12 x 10 = 120, '0' is the unit's digit in the given product. In competitive examination we get different types of questions of Unit digits like *  find the unit digit of (562)^44 *  find the unit digit of (4569)^927 x (7596)^44..... and soon. Find the unit digit of an exponential number First , divide the power of that number by 4 1.  Condition  (a):-  if you get the remainder zero then change the power of that number by 4. Example:  we have to find the unit digit of this number (3846)84, Step 1:  At first we have to divide 84 by 4 Step 2nd:  After dividing you will g...

number system is very important chapter for all  competitive  exam . everything is included in it like all numbers,some special number,divisibility concept,unit digit,divisibility remainder concept,decimal and number of factor,key to remainder concept,lcm and hcf etc. Number System:- 1)  Natural Number :-  All counting numbers are called natural numbers and it is denoted by N or number used for counting.   Example: {1, 2, 3, 4..infinity)  2)  Whole Number :-  The set of all natural number together with zero are called whole numbers and it is denoted by W or from zero to infinity.  Example:-  (0, 1, 2, 3, 4.....) 3)   Integer :-  The set of all natural numbers, zero and negative of all natural numbers are called integers and it is denoted by I and Z or all positive to negative number. Example:  ......-6,-5, -4,-3, -2, -1, 0, 1, 2, 3, 4,5,6.... * Negative integer is denoted by ={.....-5,-4,-3, -2, -1} *Positive integer is de...

Ratio and Proportion  is very important chapter for all  competitive  exam and everything is included in it like all ratio,proportion,compounded ratio,types of proportion and most important questions.             RATIO AND PROPORTION RATIO : - The ratio of two quantities x and y is the fraction a/b and we write it as x : y. In the ratio x: y, we call x as the first term or antecedent and y, the second term or consequent  i.e. ratio 4: 9 represents with antecedent =4, consequent = 9 Types of Ration duplicate ratio = a^2 : b^2 triplicate ratio = a^3 : b^3   sub-duplicate ratio= √a : √b sub-triplicate ratio= 3√a : 3√b TYPES OF PROPORTION * Fourth Proportion = ( a,b,c ) = bc/a * Third Proportion = ( a,b,c ) = (b^2)/a * Mean  Proportion =  ( a,b,c ) = root(ab)   Qes.   If p: q = 2:3 and q:r = 5:7 then what is the ratio p:q:r   Ans.       p:q=2:3           ...