a business man bought some items for 2000rs. he kept 10 items for itself and sold the remaining at a profit of 25 rs. per item from the amount he received in this deal, he could buy 15 more items find the original prize of each item
Answers
Given : A businessman bought some items for rupees 2,000
he kept 10 items for himself and sold the remaining at a profit of rupees 25 per item
from the amount he received in this deal equaled by 15 more items
To find : the original price of each item
Solution:
original price of each item = C
items Bought = 2000/C
items sold = 2000/C - 10
Selling Price of item = C + 25
=> Total SP = (2000/C - 10)(C + 25)
=> Total SP = 2000 + 50000/C - 10C - 250
=> Total SP = 1750 + 50000/C - 10C
amount he received in this deal equaled by 15 more items
=> C(2000/C + 15) = 2000 + 15C
2000 + 15C = 1750 + 50000/C - 10C
=> 25C - 50000/C + 250 = 0
=> C - 2000/C + 10 = 0
=> C² - 2000 + 10C = 0
=> C² + 10C - 2000 = 0
=> C² + 50C - 40C - 2000 = 0
=> (C + 50)(C - 40) = 0
=> C = 40
original price of each item = Rs 40
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