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Question

x and y are two articles sold by a trader.
The cost price of x equals the selling price of y.
x is sold at 25% profit, y's cost price is 25% less than it's selling price.
Find the overall profit/loss percentage made by the trader.

Solution
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C.P of x=S.P of y …………….(i)
x is sold at 25% profit =cp of x+25100×CP of x
S.P of x=125100× C.P of x...……..(ii)
C.P of y is 25% less than its S.P
C.P of y=S.P25100× S.P of y
but S.P of y=C.P of x
C.P of y=75100× C.P of x ………….(iii)
Total C.P = C.P of x + C.P of y use equation (iii)
Total S.P = S.P of y + S.P of x use equation (i) and (ii)
By equation (i), (ii) and (iii) convert everything in terms of C.P of x
Total C.P=C.P of x+75100 C.P of x=175100× C.P of x
Total S.P = C.P of x+125100× C.P of x=225100× C.P of x
Let 'r' be percentage of profit or Profit=50100× C.P of x
C.P+r% of CP= S.P r% of 175100CPx=50100CPx
175100CP×r100×175100CPx=225100CPx r=50175×100
175100(100+r100)CPx=225100CPx r=28.57%.
100+r100=225175
r=28.57%.

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