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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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PROBLEMS ON AGES,IMPORTANT QUESTIONS BASED ON AGES CONCEPTS

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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 solution:

Present age of Alok = 4/(8+5) × 52 = 16 years.




Ratio and product of ages given 


Qes. Product of present age of Sita and Gita  is 2223 years and their present age ratio is 13:19 find the difference age of Gita and Sita.


Soln. Let, age of Sita is 13x and age of Gita is 19x


Then, product of their ages = 13x × 19x = 247x² 

⇒ 247x² = 2223

⇒ x² = 9

⇒ x = 3


Therefore, 

required difference = 19x – 13x = 6x = 6 × 3 = 18 years.




Ratios of Present and future ages given 


Qes. The ratio of present age P and Q is 15:14 after 5 years their ratio will be 81:65 then find the present age of P.


Soln.  Let, present age of P = 15x and present age of Q = 14x


A/q,


(15x + 5)/(14x + 5) = 81/65


⇒ (15x + 5) × 65 = (14x + 5) × 81 


⇒ 975x + 325 = 1134x + 405 


⇒ -159x = 80


⇒ x = - ve( value )

(can not be determine because age is not in the negative)



Ratios of Past and Present Ages given 


Qes.  If 5 years ago, the ratio of age of Banti and Babli was 1 : 2 and after 15 years from present their ratio will be 5 : 6. Find the age of babli after 35 years.


Soln.  Let, present age of Banti be P and present age of Babli be Q.


A/Q,


(P - 5)/(Q - 5) = ½


⇒ 2P – 10 = Q – 5


⇒ P = (Q + 5)/2 ---- (1)


Also, (P + 15)/(Q + 15) = 5/6


⇒ 6P + 90 = 5Q + 75


⇒ 6P + 15 = 5Q 


Putting value of P from equation 1, we get


3Q + 15 + 15 = 5Q


⇒ 2Q = 30


⇒ Q = 15


∴ Age of babli after 35 years = 15 + 35 = 50 years.




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