MadeEasy Workbook: General Aptitude - Profit Loss

Question

This was one of the formula given in the "profit and loss" chapter of made eady booklet - reasoning and aptitude.

How do we derive this formula?

Answer 1

As the selling price is same 

$Let$ 

$S.P \ be \ S$ 

$C.P \  of \  1^{st} \  article \  be \  C_1$

$C.P \  of \  2^{nd} \  article \  be \  C_2$

$Profit \  on \  1^{st} \ article \ be \ P_1$

$Profit \ of \ 2^{nd} \  article \  be \  P_2$

$x = (P_{1} / C_{1})*100$

$P_1 = S - C_1$

$x = (S - C_1 / C_{1})*100$

$x/100 = S / C_{1} -1$

$C_{1} = 100.S / (100 + x)$

$y = (P_{2} / C_{2})*100$

$P_2 = S - C_2$

$y = (S - C_2 / C_{2})*100$

$y/100 = S / C_{2} -1$

$C_{2} = 100.S / (100 + y)$

$Total \ S.P = S + S = 2.S$

$Total \ C.P = C_1 + C_2$

$Total \ Profit(P) = 2.S - (C_1 + C_2)$

$z$ $= [P / (Total C.P)]*100$          \\ $z$ be the overall profit%

$z/100$ $= P / (C_1 + C_2)$

      $= (2.S - ( C_1 + C_2 ) ) / (C_1 + C_2)$

      $= 2.S / (C_1 + C_2) - 1$

      $= (2.S / (100.S/(100 + x) + 100.S/(100 + y) ) ) - 1$

      on solving we get,

      $=  [2.(100+x).(100+y)] / 100.[ (100 + x)  + (100 + y) ] - 1$

      $ = [ [2.100^2  + 200.x + 200.y + 2.x.y] - [100^2 + 100.x + 100^2 + 100.y] ] / 100.[ (100 + x)  + (100 + y) ]$

      $= [100.x + 100.y + 2.x.y] / 100.[ (100 + x)  + (100 + y) ]$

      $= [100.(x+y) + 2.x.y] / 100.[ (100 + x)  + (100 + y) ]$

$z = [100.(x+y) + 2.x.y] / [ (100 + x)  + (100 + y) ] $

same holds for overall loss%