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 amountthen cost of each book $=\frac{80}{x+4}$Step 2: Finding the number of books he boughteach book would have cost $\mathrm{Rs}.1$ less, then we get $⇒\frac{80}{x}-\frac{80}{x+4}=1\phantom{\rule{0ex}{0ex}}⇒\frac{80x+320-80x}{x\left(x+4\right)}=1\phantom{\rule{0ex}{0ex}}⇒{x}^{2}+4x-320=0\phantom{\rule{0ex}{0ex}}⇒{x}^{2}+\left(20-16\right)x-320=0\phantom{\rule{0ex}{0ex}}⇒{x}^{2}+20x-16x-320=0\phantom{\rule{0ex}{0ex}}⇒x\left(x+20\right)-16\left(x+20\right)=0\phantom{\rule{0ex}{0ex}}⇒\left(x-16\right)\left(x+20\right)=0\phantom{\rule{0ex}{0ex}}⇒x=16,-20$Number of books cannot be negative Therefore number of books shopkeeper buy is $16$

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