Question

a shopkeeper purchased some balls of rs 600. 10 balls were given to his son and the remaining balls were sold at a profit of 5rs per ball. from the amount received in this deal he purchased 15 more balls . find the original price of each ball

Answer 1

Let Original price of each item = Rs. x

And

In starting we buy total number of item = y , So from given " A businessman bought some items for rs. 600 . " We get

xy = 600 --------------- ( 1 )

And

As given " keeping ten items for himself he sold the remaining items at a profit of rs. 5 per item. From the amount received in this deal he could buy 15 more items . "

We get

( y - 10 ) ( x + 5 ) = x ( y + 15 )

xy - 10 x + 5y - 50 = x y + 15x

- 25 x + 5y - 50 = 0

25 x - 5y + 50 = 0

5 x - y + 10 = 0 , Now we substitute y = 600/x

from equation 1 we get

5 x - 600/x + 10 = 0

5x2 + 10x - 600 = 0

x2 + 2x - 120 = 0

x2 + 12x - 10x - 120 = 0

x ( x + 12 ) - 10 ( x + 12 ) = 0

( x + 12 ) ( x - 10 ) = 0

So,

x = 10 , -12

And we assume x as original price of each item , So rate can't be negative , So we neglect x = - 12 , and we get

x = 10

So,

Original rate of each item = Rs . 10