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PERCENTAGES CONCEPTS,FORMULAS,DEFINITIONS,EXAMPLES,TRICKS

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    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) % ...
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NUMBER SYSTEM CONCEPTS,FORMULAS,DEFINITIONS,EXAMPLES,TRICKS PART-3

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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...
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