A person sells a book for Rs.11. He gains as many percent as its cost price in rupees. What is the cost price?Options40201030

The problem states that the gain percentage is equal to the cost price.

Let's denote the cost price as 'x'.

According to the problem, the selling price is the cost price plus the gain. The gain is x% of the cost price, which is (x/100)*x.

So, the selling price is x + (x/100)*x = Rs.11.

Solving this equation will give us the cost price 'x'.

Let's simplify the equation:

x + (x^2)/100 = 11

Multiply all terms by 100 to get rid of the denominator:

100x + x^2 = 1100

Rearrange the terms:

x^2 + 100x - 1100 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0.

We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

In this case, a = 1, b = 100, and c = -1100.

Substituting these values into the quadratic formula gives:

x = [-100 ± sqrt((100)^2 - 41(-1100))] / (2*1) x = [-100 ± sqrt(10000 + 4400)] / 2 x = [-100 ± sqrt(14400)] / 2 x = [-100 ± 120] / 2

This gives two possible solutions: x = 10 or x = -220.

Since the cost price cannot be negative, the cost price of the book is Rs.10.