gvishesh21 wrote:
What is the profit percent if an article is sold without any discount on the original selling
price?
(1) If the article is sold at x% discount on the original selling price, there is x% profit.
(2) If the article is sold at \(\frac{5x}{4}\)% discount on the original selling price, there is \(\frac{x}{2}\)% profit.
Quick answerStatement 1 will give one equation of original selling price and cost price in x, but we do not know x. Insufficient
Statement 2 will give another equation of original selling price and cost price in x, but we do not know x. Insufficient
Combined: Two equations of s/c and x. Sufficient
C
Proper method in PSLet the selling price be s and cost price be c, then we are looking for \(\frac{s-c}{c}*100\) or \((\frac{s}{c}-1)*100\)
(1) If the article is sold at x% discount on the original selling price, there is x% profit.
\(s(\frac{100-x}{100})=c(\frac{100+x}{100})\)
\(s(100-x)=c(100+x)............\frac{s}{c}=\frac{100+x}{100-x}\)
Insufficient
(2) If the article is sold at \(\frac{5x}{4}\)% discount on the original selling price, there is \(\frac{x}{2}\)% profit.
\(s(\frac{100-\frac{5x}{4}}{100})=c(\frac{100+\frac{x}{2}}{100})\)
\(\frac{s}{c}=\frac{100+\frac{x}{2}}{100-\frac{5x}{4}}=\frac{400+2x}{400-5x}\)
Insufficient
Combined
\(\frac{200+x}{100-5x}=\frac{100+x}{100-x}\)
\((400+2x)(100-x)=(100+x)(400-5x)\)
\(40000-200x-2x^2=40000-5x^2-100x\)
\(3x^2=100x\)
so, either x=0, or 3x=100, that is x=\(\frac{100}{3}\)
Now, \(\frac{s}{c}=\frac{100+\frac{100}{3}}{100-\frac{100}{3}}=\frac{400}{200}=2\)
Thus, profit % = \((\frac{s}{c}-1)*100=(2-1)*100=200\)
C
May be the question should have mentioned that original selling price and cost price are different.