Question

A shopkeeper sells two T.V. sets at the same price. There is a gain of $20\%$ on one TV. and loss of $20\%$ on the other. State which of the following statements is correct

• A. The shopkeeper neither gains nor loses
• B. The shopkeeper loses by $2\%$
• C. The shopkeeper gains by $4\%$
• D. The shopkeeper loses by $4\%$

Answer 1

The correct option is D The shopkeeper loses by $4\%$

Let the S.P. of both the T.V sets be Rs. $x$.

Then, C.P. of the T.V set at a gain of $20\%$ $=$ Rs. $\frac{100\times x}{120}=$ Rs. $\frac{5x}{6}$

C.P. of the T.V set at a loss of $20\%$ $=$ Rs. $\frac{100\times x}{80}=$ Rs. $\frac{5x}{4}$

Total C.P. $=$ Rs. $(\frac{5x}{6}+\frac{5x}{4})=$ Rs. $\frac{10x+15x}{12}=$ Rs. $\frac{25x}{12}$

Total S.P. $=$ Rs. $2x$

Loss $=$ Rs. $(\frac{25x}{12}-2x)=$Rs. $\frac{x}{12}$

Loss $\%$ $=\frac{\frac{x}{12}}{\frac{25x}{12}}\times 100=4$ $\%$