Question

Question #2817d

Answer 1

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, `(x+4).(80/x-1) = 80`

`rArr x. 80/x-x+4. 80/x-4 =80`

`rArr 80-x+320/x-4=80`

`rArr -x+320/x=80-80+4`

`rArr -x+320/x=4`

`rArr [-x^2+320]/x=4`

`rArr -x^2+320 = 4x`

`rArr -x^2+320-4x=0`

`rArr -(x^2+4x-320)=0`

`rArr x^2+4x-320 = 0` [Divide by -1 in both sides]

`rArr x^2+20x-16x-320=0`

`rArr x(x+20)-16(x+20)=0`

`rArr (x+20)(x-16)=0`

`rArr x+20 =0, x-16=0`

`rArr x = -20, 16` [ x cannot be - 20 ]

`rArr x = 16`

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