A local library purchased several biography books and mystery novels for their new collection. The library spent exactly ₹4,800 on biography books and ₹4,800 on mystery novels. Each biography book costs ₹40 more than a mystery novel. The library was able to buy 10 more mystery novels than biography books. Find the number of biography books purchased.
30
Let the number of biography books be n, costing c each, so \(nc=4800\).
Mystery novels number \(n+10\), costing \(c-40\) each, so \((n+10)(c-40)=4800\).
Substituting \(c=\tfrac{4800}{n}\) and simplifying gives \(n^2+10n-1200=0\).
Solving this quadratic: \(n = \dfrac{-10+\sqrt{100+4800}}{2} = \dfrac{-10+70}{2}=30\).
Hence, the number of biography books purchased is 30.
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