Question

I sold a book at a loss of $8\%$. Had i sold it for Rs $120$ more, $7\%$ would have been gained. Find the cost price of the book.

• A. Rs $900$
• B. Rs $800$
• C. Rs $600$
• D. Rs $750$

Answer 1

The correct option is B Rs $800$

Let the cost price of the book is Rs r

We know that Loss $\%=\frac{CP-SP}{100}\Rightarrow 8\%=\frac{r-SP}{r}\Rightarrow \frac{8}{100}=\frac{r-SP}{r}\Rightarrow 8r=100(r-SP)\Rightarrow 8r-100r=-100SP\Rightarrow -92r=-100SP\Rightarrow SP=\frac{-92r}{-100}\Rightarrow S.P.=0.92r$

We know that Gain $\%=\frac{SP-CP}{100}\Rightarrow 7\%=\frac{(0.92r+120)-r}{r}\Rightarrow \frac{7}{100}=\frac{0.92r+120-r}{r}\Rightarrow 7r=100(0.92r+120-r)\Rightarrow 7r=100(-0.08r+120)\Rightarrow 7r=-8r+12000\Rightarrow 15r=12000\Rightarrow r=\frac{12000}{15}=800Rs$

Option B is the correct answer.