Question

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.

• A. 15
• B. 25
• C. 35
• D. 45

Answer 1

The correct option is B 25

SP of trader $A=1000(1+\frac{x}{100})=1000+10x$
Profit of trader A = 10x
MP of trader B $=2000(1+\frac{2x}{100})=2000+40x$
SP of trader $B=2000(1+\frac{2x}{100})(1-\frac{x}{100})=2000(1+\frac{x}{100}-\frac{2x^2}{{100}^2})=2000+20x+0.4x^2$
Profit of trader B = 0.4x${}^2$ + 20x
Both make the same profit $\Rightarrow 10x=-0.4x^2+20x\Rightarrow 0.4x^2=10x\Rightarrow 0.4x=10\Rightarrow x=25\Rightarrow x=25\%$