A bookseller sells a book at a profit of 10%. If he had bought it at 4% less and sold it for Rs. 6 more, he would have gained $$18\frac{3}{4}$$ % The cost price of the book is

Let cost price of the book = Rs. $$100x$$

Profit % = 10%

=> Selling price = $$\frac{10}{100}\times100x=Rs.$$ $$110x$$

Now, new cost price = $$C'=100x-(\frac{4}{100}\times100x)=Rs.$$ $$96x$$

Similarly, new selling price = $$S'=Rs.$$ $$(110x+6)$$

=> Profit % = $$\frac{(S'-C')}{C'}\times100=18\frac{3}{4}$$

=> $$\frac{(110x+6)-96x}{96x}\times100=\frac{75}{4}$$

=> $$\frac{14x+6}{96x}=\frac{75}{4}\times\frac{1}{100}$$

=> $$\frac{14x+6}{96x}=\frac{3}{16}$$

=> $$14x+6=\frac{3}{16}\times(96x)$$

=> $$14x+6=18x$$

=> $$18x-14x=4x=6$$

=> $$x=\frac{6}{4}=1.5$$

$$\therefore$$ Cost price = $$100\times1.5=Rs.$$ $$150$$

=> Ans - (C)