Question

(ii) A businessman bought some items for 2000. He kept 10 items for himself and
sold the remaining at a profit of 25 per item. From the amount he received in this
deal, he could buy 15 more items. Find the original price of each item.​

Answer 1

Answer:

Let the number of items bought be x.

Therefore, the cost per item bought = 600/x.

Let the number of the items sold be y.

Since (x - 10) items were sold, the selling price per item = y/(x-10).

Since the selling price per item includes a 5 Rs. profit, then:

cost price per item + profit per item = selling price per item:

600/x + 5 = y/(x-10) (i)

Since the proceeds from selling the y items can be used to purchase 15 items, then:

y = cost price per item multiplied by 15:

y = 600/x * 15 (ii)

Substituting for y in equation (i), we get:

600/x + 5 = (600/x) * 15/(x-10)

600/x + 5 = 9000/(x*(x-10))

5 = 9000/(x*(x-10) - 600/x

5 = (9000 - 600(x-10))/(x*(x-10))

5(x*(x-10)) = 9000 - 600x + 6000

5x^2 - 50x + 600x - 15000 = 0

x^2 - 10x + 120x - 3000 = 0

x^2 + 110x - 3000 = 0

Using the quadratic formula:

ax^2 +bx + c = 0,

x =( -b +/- (sqrt(b^2 - 4*a*c)))/2*a, we have:

x = (- 110 +(110^2 - 4*1*-3000)^.5)/2*1, or x = (- 110- (110^2 - 4*1*-3000)^.5)/2*1

x = 22.62, or x = -132.62