# Question #2817d

Oct 14, 2017

16 and 5

#### Explanation:

Let shopkeeper buys x books for Rs. 80.
So, 1 book costs Rs. 80/x.

If he buys (x + 4) books and then each book costs ( 80/x - 1).
So, (x + 4) books cost = Rs. ( x + 4 ).(80/x - 1)

As per question, $\left(x + 4\right) . \left(\frac{80}{x} - 1\right) = 80$

$\Rightarrow x . \frac{80}{x} - x + 4. \frac{80}{x} - 4 = 80$

$\Rightarrow 80 - x + \frac{320}{x} - 4 = 80$

$\Rightarrow - x + \frac{320}{x} = 80 - 80 + 4$

$\Rightarrow - x + \frac{320}{x} = 4$

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

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

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

$\Rightarrow - \left({x}^{2} + 4 x - 320\right) = 0$

$\Rightarrow {x}^{2} + 4 x - 320 = 0$ [Divide by -1 in both sides]

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

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

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

$\Rightarrow x + 20 = 0 , x - 16 = 0$

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

$\Rightarrow x = 16$

No. of books = 16 and Each book buys Rs.80/16 = Rs. 5/-