$A$ sold an article to $B$ at a loss of $20 %,$ and $B$ sold it to $C$ at a profit of $20 % .$ If $A$ had sold the article for the price $C$ paid, what would have been his loss or gain per cent ?

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Solution

Let original price be $x$
A sold at a loss at $20$ % i.e $\frac{80}{100} \times x = \frac{4 x}{5}$
B sold at a point of $20$ % i.e $\frac{4 x}{5} + \frac{20}{100} \times \frac{4 x}{5} = \frac{4 x}{5} (1 + \frac{1}{5}) = \frac{6 x}{5} \times \frac{4}{5} = \frac{24 x}{25}$
If A had sold at a price of $\frac{24 x}{25}$
He would have a loss of $\frac{x - \frac{24 x}{25}}{x} \times 100 = \frac{1}{25} \times 100 = 4$ % loss.

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A sold an article to B at a loss of 20%, and B sold it to C at a profit of 20%. If A had sold the article for the price C paid, what would have been his loss or gain per cent ?

Let original price be xA sold at a loss at 20% i.e 80100×x=4x5B sold at a point of 20% i.e 4x5+20100×4x5=4x5(1+15)=6x5×45=24x25If A had sold at a price of 24x25He would have a loss of x−24x25x×100=125×100=4% loss.

$A$ sold an article to $B$ at a loss of $20 %,$ and $B$ sold it to $C$ at a profit of $20 % .$ If $A$ had sold the article for the price $C$ paid, what would have been his loss or gain per cent ?