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.

Answer 1

C.P of x$=$S.P of y …………….(i)

x is sold at $25\%$ profit $=$cp of $x+\frac{25}{100}\times CP$ of x

$\therefore$ S.P of $x=\frac{125}{100}\times$ C.P of x...……..(ii)

C.P of y is $25\%$ less than its S.P

C.P of y$=$S.P$-\frac{25}{100}\times$ S.P of y

but S.P of $y=$C.P of x

C.P of $y=\frac{75}{100}\times$ C.P of x ………….(iii)

Total C.P $=$ C.P of x $+$ C.P of y $\to$ use equation (iii)

Total S.P $=$ S.P of y $+$ S.P of x$\to$ 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 $x+\frac{75}{100}$ C.P of x$=\frac{175}{100}\times$ C.P of x

Total S.P $=$ C.P of $x+\frac{125}{100}\times$ C.P of $x=\frac{225}{100}\times$ C.P of x

Let 'r' be percentage of profit or Profit$=\frac{50}{100}\times$ C.P of x

C.P$+r\%$ of CP$=$ S.P $r\%$ of $\frac{175}{100}C{P}_x=\frac{50}{100}C{P}_x$

$\frac{175}{100}CP\times \frac{r}{100}\times \frac{175}{100}C{P}_x=\frac{225}{100}C{P}_x$ $r=\frac{50}{175}\times 100$

$\frac{175}{100}\left(\frac{100+r}{100}\right)C{P}_x=\frac{225}{100}C{P}_x$ $r=28.57\%$.

$\frac{100+r}{100}=\frac{225}{175}$

$r=28.57\%$.