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 -

Solution(By Examveda Team)

Let C.P. of the book be Rs. 100
Profit = 10%. S.P. = Rs. 110
New C.P. = 4% less = Rs. 96
If gain is $$18\frac{3}{4}\%$$
$$\eqalign{ & {\text{Then S}}{\text{.P}}{\text{.}} \cr & = \left( {118\frac{3}{4}\% {\text{ of Rs}}{\text{. }}96} \right) \cr & = {\text{Rs}}.\left( {\frac{{475}}{4} \times \frac{1}{{100}} \times 96} \right) \cr & = {\text{Rs}}{\text{. }}114 \cr} $$
Difference in S.P. = Rs. (114 - 110) = Rs. 4
If difference in S.P. is Rs. 4, C.P. = Rs. 100
If difference in S.P. is Rs. 6,
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{4} \times 6} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}150 \cr} $$