SOLUTION: a man bought a certain number of toys for Rs.180. he kept one for his own use and sold the rest for one rupee each more than he gave for them. Besides getting his own toy for nothi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a man bought a certain number of toys for Rs.180. he kept one for his own use and sold the rest for one rupee each more than he gave for them. Besides getting his own toy for nothi      Log On


   

Question 933084: a man bought a certain number of toys for Rs.180. he kept one for his own use and sold the rest for one rupee each more than he gave for them. Besides getting his own toy for nothing, he made a profit of Rs 10. find the number of toys, he intially bought.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A man bought N toys for Rs180.
Each toy cost him Rs180%2FN

He kept 1 for his own use and sold the other N-1 toys for Rs%28180%2FN%2B1%29. 
Selling N-1 toys for Rs%28180%2FN%2B1%29 he received Rs%28N-1%29%2A%28expr%28180%2FN%29%2B1%29

he made a profit of Rs10, and he paid Rs180, So he received Rs180+Rs10 = Rs190.
So   

Rs%28N-1%29%2A%28expr%28180%2FN%29%2B1%29%22%22=%22%22Rs190
%28N-1%29%2A%28180%2FN%2B1%29%29%22%22=%22%22190  
%28N%29%28180%2FN%29%2B%28N%29%281%29%2B%28-1%29%28180%2FN%29%2B%28-1%29%281%29%22%22=%22%22190
%28cross%28N%29%29%28180%2Fcross%28N%29%29%2BN-180%2FN-1%22%22=%22%22190
180%2BN-180%2FN-1%22%22=%22%22190
179%2BN-180%2FN%22%22=%22%22190
Multiply all terms by N
179N%2BN%5E2-180%22%22=%22%22190N
This is a quadratic equation, get 0 on the right:
-11N%2BN%5E2-180%22%22=%22%220
Write terms in descending order:
N%5E2-11N-180%22%22=%22%220
Factor:
%28N%2B9%29%28N-20%29%22%22=%22%220
N%2B9=0, N-20=0
cross%28N=-9%29, N=20

He intially bought 20 toys.

Edwin