A person sells a book for Rs.11.He gains as many percent as its cost price in rupees.What is the cost price?

Step 1: Let's denote the cost price of the book as 'x' rupees.

Step 2: According to the problem, the person gains as many percent as the cost price. This means the gain is 'x' percent of the cost price.

Step 3: We know that gain percent is calculated as (Gain/Cost Price)*100. So, we can write the equation as x = (Gain/x)*100.

Step 4: The selling price of the book is given as Rs.11 and we know that Selling Price = Cost Price + Gain. So, we can write another equation as 11 = x + Gain.

Step 5: Now we have two equations and two variables. We can solve these equations simultaneously to find the value of 'x'.

Step 6: From equation 4, we can express Gain as 11 - x.

Step 7: Substituting this value in equation 3, we get x = ((11 - x)/x)*100.

Step 8: Simplifying this equation, we get x^2 = 1100 - 100x.

Step 9: Rearranging the terms, we get x^2 + 100x - 1100 = 0.

Step 10: This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve this equation using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Step 11: Substituting the values, we get x = [-100 ± sqrt((100)^2 - 41(-1100))] / (2*1).

Step 12: Simplifying further, we get x = [-100 ± sqrt(10000 + 4400)] / 2.

Step 13: Simplifying further, we get x = [-100 ± sqrt(14400)] / 2.

Step 14: Simplifying further, we get x = [-100 ± 120] / 2.

Step 15: We get two solutions x = 10 and x = -110. But cost price cannot be negative. So, the cost price of the book is Rs.10.