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A trader bought a number of …

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A trader bought a number of articles for Rs.900. Five articles were found damaged. He sold 
each of the remaining articles at Rs.80 in the whole transaction. Find the number of articles he 
bought.

  • 1 answers

Sia ? 4 years, 10 months ago

Let number of articles he bought be x, and cost of each article be y.
Therefore, cost of x articles  = xy = 900 {tex}\Rightarrow{/tex} y = {tex}\frac{900}{x}{/tex}
According to given information we have,
(x - 5)({tex}\frac{900}{x}{/tex} + 2) = 900 + 80
{tex}\Rightarrow{/tex}{tex}\frac { 900 x + 2 x ^ { 2 } - 4500 - 10 x } { x }{/tex} = 980 
{tex}\Rightarrow{/tex} 2x2 + 890x - 4500 = 980x
{tex}\Rightarrow{/tex}2x2 - 90x- 4500 = 0
{tex}\Rightarrow{/tex}x2 - 45x - 2250 = 0
By factorization, we have, 
 D= b2​​​​​​-4ac
D= (-45)2 -4×1 (-2250)
D= 2025+ 9000
D=11025
x1 =-(-45)+105/2 , x2 = -(-45) -105/2
X1= 75, x=-75
​​​​​​since, the number of articles can not be negative,
So, x=75
{tex}\therefore{/tex} Number of articles = 75

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