Question

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. How many books did he buy? [4 MARKS]

Answer 1

Framing of equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the number of books bought be $x$. Then,

Cost of $x$ books $=Rs.80\Rightarrow$ Cost of one book $=Rs\frac{80}{x}$

If the number of books bought is $x+4$, then

Cost of one book $=Rs\frac{80}{x+4}$

It is given that the cost of one book is reduced by one rupee.

$\therefore \frac{80}{x}-\frac{80}{x+4}=1$

$\Rightarrow 80(\frac{1}{x}-\frac{1}{x+4})=1$

$\Rightarrow 80\left\{\frac{x+4-x}{x(x+4)}\right\}=1$

$\Rightarrow \frac{320}{x^2+4x}=1$

$\Rightarrow x^2+4x=320$

$\Rightarrow x^2+4x-320=0$

$\Rightarrow x^2+20x-16x-320=0$

$\Rightarrow x(x+20)-16(x+20)=0$

$\Rightarrow (x+20)(x-16)=0$

$\Rightarrow x=-20or,x=16\Rightarrow x=16$ [$\because x$ cannot be negative]

Hence, the number of books is 16