Question

Businessman bought some items for rupees 7500 he kept five items for himself and sold the remaining item at a profit of rupees 30 per item from the amount received in this deal he could buy for more items find original price of each item​

Answer 1

hey mate!

No. of items bought = x

Price per item = y

Total amount paid = x * y = xy = 7500

y = 7500 / x

Total items sold = (x - 5)

Price of each item = (y + 30)

Total revenue received = (x - 5) * (y + 30)

Since he can buy 4 more items from his revenue

(x - 5)(y + 30) - 7500 = 4 * y

(x - 5)[(7500/x) + 30] - 7500 = 4y

(x - 5)[(7500 + 30x) / x ] - 7500 = 4y

(x - 5)(7500 + 30x) - 7500x  = 4xy

7500x + 30x² - 37500 - 150x - 7500x = 4xy

30x² + 7500x - 150x - 7500x  - 37500 = 4(7500)

30x² - 150x - 37500 - 30000 = 0

30x² - 150x - 67500 = 0

30 (x² - 5x- 2250) = 0

x² - 5x - 2250 = 0

x = -45 , +50 (Solving quadratic equation)

Since cost cannot be negative, so x = 50 which is the number of items bought.

The price per item = 7500/50 = 150

Hope This Helps :)