a person sells a book for rs. 11. he gains as many percent as its cost price in rupees. what is the cost price?

June 28, 2026

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.

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