On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book, in rupees?

Let the cost price of the pen be P and the cost price of the book be B. Using the profit formula, the first scenario yields 0.95P plus 1.15B equals P plus B plus 7, which simplifies to negative 0.05P plus 0.15B equals 7. The second scenario yields 1.05P plus 1.10B equals P plus B plus 13, which simplifies to 0.05P plus 0.10B equals 13. Adding these two simplified equations cancels out P and results in 0.25B equals 20, so B equals 80. The cost price of the book is 80 rupees.

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