Let CP be the cost price in rupees. The book is sold for Rs. 11, with a profit percentage equal to CP (so profit is CP100×CP=CP2100\frac{CP}{100}\times CP=\frac{CP^2}{100}100CP​×CP=100CP2​). Thus, selling price = CP + profit, or 11=CP+CP210011=CP+\frac{CP^2}{100}11=CP+100CP2​.

Solving the Equation

Multiply both sides by 100: 1100=100×CP+CP21100=100\times CP+CP^21100=100×CP+CP2. Rearrange into quadratic form: CP2+100×CP−1100=0CP^2+100\times CP-1100=0CP2+100×CP−1100=0.

Factorize: (CP+110)(CP−10)=0(CP+110)(CP-10)=0(CP+110)(CP−10)=0. Solutions: CP = -110 (invalid, as cost price can't be negative) or CP = 10.

Verification

If CP = Rs. 10, profit % = 10%, so profit = 10100×10=\frac{10}{100}\times 10=10010​×10= Rs. 1. Selling price = 10 + 1 = Rs. 11, which matches.

TL;DR: The cost price is Rs. 10.

Information gathered from public forums or data available on the internet and portrayed here.