Question

A shopkeeper buys some books for rs. 80. If he had bought 4 more books for the same amount, each book would have cost rs. 1 less. Find the number of books he bought.A shopkeeper buys some books for rs. 80. If he had bought 4 more books for the same amount, each book would have cost rs. 1 less. Find the number of books he bought.

Answer 1

$\huge\text{\underline{\underline{Solution:}}}$


Let the number of books bought be $\bold{'x'.}$


$\bold{\underline{\underline{So,}}}$


The cost of each book = Rs. $\bold{\frac{80}{x}}$


If he would have bought $\bold{4}$ more books,


$\text{\underline{\underline{Then,}}}$


The cost of each book = Rs. $\bold{\frac{80}{(x + 4)}}$


$\text{\underline{\underline{According\:to\:the\:question,}}}$


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


$\frac{(80x + 320 - 80x)}{( {x}^{2} + 4x) } = 1$


${x}^{2} + 4x = 320$


${x}^{2} + 4x - 320 = 0$


${x}^{2} + 20x - 16x - 320 = 0$


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


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


$x + 20 = 0 \: \: \: \:$ $\bold{\underline{\underline{OR}}}$ $\: \: \: \: x - 16 = 0$


$x = 0 - 20 \: \: \: \:$ $\bold{\underline{\underline{OR}}}$ $\: \: \: \: x = 0 + 16$


$x = - 20 \: \: \: \: \: \: \: \:$ $\bold{\underline{\underline{OR}}}$ $\: \: \: \: x = 16$


$\text{\underline{\underline{Therefore,}}}$


As, number of books cannot be negative, so, $\bold{x\:=\:-20}$ is discarded.


$\text{\underline{\underline{Hence,}}}$


The number of books he bought = $\bold{16.}$

Answer 2

$<b>$

Let the number of books bought be 'x'
So,

If he would have bought 4 more books, 

The cost of each book = Rs. ${\frac{80}{(x + 4)}}​$

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

$\frac{(80x + 320 - 80x)}{( {x}^{2} + 4x) }$ = 1​(x​2​​+4x)​​(80x+320−80x)​​=1 

{x}^{2} + 4x = 320x​2​​+4x=320 

{x}^{2} + 4x - 320 = 0x​2​​+4x−320=0 

${x}^{2}$+ 20x - 16x - 320 = 0x​2​​+20x−16x−320=0 

x(x + 20) - 16(x + 20) = 0x(x+20)−16(x+20)=0 

(x + 20)(x - 16) = 0(x+20)(x−16)=0 

x + 20 = 0 OR x−16=0 

x = 0 - 20 0R x = 0 + 16

x=−20 OR
x = 16x=16 

As, number of books cannot be negative, so, 
x=-20 is discarded. 

The number of books he bought = 16.