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 equalled by 15 more items find the original price 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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Step-by-step explanation:
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 he could buy 15 more items find the original price of each item
- Let the items bought by businessman be m
- So Cost Price of m items is Rs 2000
- So Cost Price of each item will be 2000 / m
- According to the question, he kept 10 items to himself and sold remaining at a profit of 25 per item.
- Profit = Rs 25
- So items left will be m – 10
- Now S.P = C.P + Profit.
- S.P = (m – 10 ) x 2000 / m + 25 = (m – 10) [(2000 + 25 m ) / m
- Now he could buy 15 more items
- So from given S.P he can buy total of m + 15 items from S.P.
- Therefore ,
- (m – 10) [2000 + 25 m] / m = (2000/m) (m + 15)
- (m – 10) (2000 + 25 m) = 2000 x (m + 15)
- 2000 m – 2000 + 25 m^2 – 250m = 2000 m + 30,000
- 25 m^2 – 250 m – 50,000 = 0
- m^2 – 10 m – 2000 = 0
- m^2 – 50m + 40 m – 2000 = 0
- m(m – 50) + 40 (m – 50) = 0
- (m – 50) (m + 40) = 0
- m = 50 , - 40
- So total items he bought is 50
- Therefore original price of each item will be 2000 / 50 = Rs 40
Reference link will be
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