A book seller 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 183/4 % . The cost price of the book is = ?

Answer: Option C

Let the CP of the book = x
Gain = 10%
SP  = $$\frac{110\text{x}}{100}$$
If he had bought it at 4% less and sold it for Rs 6 more,
$$\begin{array}{rl}& \text{CP}=\frac{96x}{100}\\ & \text{SP}=\frac{110x}{100}+6\\ & \text{Gain}=\left(\frac{110x}{100}+6\right)-\frac{96x}{100}\\ & =\left(\frac{14x}{100}\right)+6\end{array}$$
Now, the gain =$$18\frac{3}{4}\%=\frac{75}{4}\%$$
Therefore,
$$\begin{array}{rl}& \Rightarrow \frac{14x}{100}+6=\frac{96x}{100}\times \frac{75}{400}\\ & \Rightarrow \frac{14x}{100}+6=\frac{96x}{4}\times \frac{3}{400}\\ & \Rightarrow 14x+600=\frac{96x}{4}\times \frac{3}{4}\\ & \Rightarrow 14x+600=6x\times 3\\ & \Rightarrow 14x+600=18x\\ & \Rightarrow 18x-14x=600\\ & \Rightarrow 4x=600\\ & \therefore x=150\end{array}$$