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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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PARTNERSHIP ,CONCEPTS,FORMULAS,DEFINITIONS,EXAMPLES,TRICKS

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 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 Time Periods,


P₁ : P₂ = C₁ : T₁ = C₂ : T₂


Here,

P= Profit, C= Capital and T=Time Period



Qes. A, B and C entered into the partnership. A contributes Rs. 28,000 for 5 months, B contributes Rs. 56,000 for 7 months and C contributes Rs. 42,000 for 4 months. If the total profit made is Rs. 25,000 then find the profit of C.


Soln.  P₁: P₂ : P3 = C₁ : T₁ = C₂ : T₂ = C3 : T3


          P₁: P₂ : P3 =


 28,000 x 5 : 56,000 x 7 : 42,000×4= 5 : 14 : 6


 The Profit Of C = [6 ÷ (5+14+6)] × 25000


  The Profit Of C = 600




Qes. A, B and C rented a meadow. A puts 20 cows for 8 months, B puts 42 cows for 4 months and C puts 28 cows for 12 months. If the rent of the meadow is Rs.3320, how much must C pay  as his share of rent?


Soln.  A :B :C=20 x 8 : 42 x 4 : 28 x 12


          A :B :C = 20 : 21 : 42


         Share of C=

        [42 ÷ ( 20+21+42 )] × 3320 = 1680 rs



Qes. A and B started a business and the ratio of their investment is 5:7. They decided that 60% of the profit will be divided into equal parts and rest of the profit will be divided into the ratio of their investments. If B got Rs.1000 more than A, find the total profit.


Soln. Let the total profit earned be P.


A/Q


(2 / 12 ) × 40P / 100 = 1000


Or,  P = 15000 rs



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