Question

A shopkeeper buys a number of books for $\mathrm{Rs}.80$. If he had bought $4$ more for the same amount each book would have cost $\mathrm{Rs}.1$ less. How many books did he buy?

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Solution

**Step 1: Finding the cost of each book **

Let a shopkeeper buys a $\text{'}x\text{'}$ number of books for $\mathrm{Rs}.80$.

Cost of each book $=\frac{80}{x}$

If he bought $4$ more books that is $\left(x+4\right)$ for the same amount

then cost of each book $=\frac{80}{x+4}$

**Step 2: Finding the number of books he bought**

each book would have cost $\mathrm{Rs}.1$ less, then we get

$\Rightarrow \frac{80}{x}-\frac{80}{x+4}=1\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{80x+320-80x}{x(x+4)}=1\phantom{\rule{0ex}{0ex}}\Rightarrow {x}^{2}+4x-320=0\phantom{\rule{0ex}{0ex}}\Rightarrow {x}^{2}+(20-16)x-320=0\phantom{\rule{0ex}{0ex}}\Rightarrow {x}^{2}+20x-16x-320=0\phantom{\rule{0ex}{0ex}}\Rightarrow x(x+20)-16(x+20)=0\phantom{\rule{0ex}{0ex}}\Rightarrow (x-16)(x+20)=0\phantom{\rule{0ex}{0ex}}\Rightarrow x=16,-20$

Number of books cannot be negative

**Therefore number of books shopkeeper buy is **$16$

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