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Let the number of books Anirudh bought = \[x\]

Given that the total cost of the books = Rs. 60

So, cost of each book = \[{\text{Rs}}{\text{.}}\dfrac{{60}}{x}\]

Also given that if Anirudh had bought 5 more books i.e., \[x + 5\] books the cost would be the same i.e., Rs. 60.

So, cost of each book if he had bought = \[{\text{Rs}}{\text{.}}\dfrac{{60}}{{x + 5}}\]

In the question, given that

The cost of each book he had already bought â€“ the cost of each book if he had bought = Rs. 1

So, we have

\[ \Rightarrow \dfrac{{60}}{x} - \dfrac{{60}}{{x + 5}} = 1 \\

\Rightarrow \dfrac{{60\left( {x + 5} \right) - 60\left( x \right)}}{{x\left( {x + 5} \right)}} = 1 \\

\Rightarrow 60x + 60\left( 5 \right) - 60x = x\left( {x + 5} \right) \\

\Rightarrow 300 = {x^2} + 5x \\

\Rightarrow {x^2} + 5x - 300 = 0 \]

Splitting and taking the terms common, we have

\[\Rightarrow {x^2} + 20x - 15x - 300 = 0 \\

\Rightarrow x\left( {x + 20} \right) - 15\left( {x + 20} \right) = 0 \\

\Rightarrow \left( {x - 15} \right)\left( {x + 20} \right) = 0 \\

\Rightarrow x = 15{\text{ or }} - 20 \]

Since the number of books can`t be a negative value, we have \[x = 15\].

Therefore, the cost of each book he had already bought \[ = \dfrac{{60}}{x} = \dfrac{{60}}{{15}} = {\text{Rs}}{\text{.4}}\]

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