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 $$18\frac{3}{4}$$% . The cost price of the book is = ?

Solution(By Examveda Team)

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,
$$\eqalign{ & {\text{CP}} = \frac{{96x}}{{100}} \cr & {\text{SP}} = \frac{{110x}}{{100}} + 6 \cr & {\text{Gain}} = \left( {\frac{{110x}}{{100}} + 6} \right) - \frac{{96x}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{14x}}{{100}}} \right) + 6 \cr} $$
Now, the gain =$$18\frac{3}{4}\% = \frac{{75}}{4}\% $$
Therefore,
$$\eqalign{ & \Rightarrow \frac{{14x}}{{100}} + 6 = \frac{{96x}}{{100}} \times \frac{{75}}{{400}} \cr & \Rightarrow \frac{{14x}}{{100}} + 6 = \frac{{96x}}{4} \times \frac{3}{{400}} \cr & \Rightarrow 14x + 600 = \frac{{96x}}{4} \times \frac{3}{4} \cr & \Rightarrow 14x + 600 = 6x \times 3 \cr & \Rightarrow 14x + 600 = 18x \cr & \Rightarrow 18x - 14x = 600 \cr & \Rightarrow 4x = 600 \cr & \therefore x = 150 \cr} $$