# A trader bought articles for 900, 5 were damaged and he sold each of the rest at 2 more than what he paid. If the profit was 80 how may articles were bought. The trader bought some articles for 900. 5 of them were damaged and the rest were sold for 2 more than what they were bought for for a profit of 80.

Let the number of articles bought initially be X. Each of them cost 900/X.

X - 5 were sold...

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The trader bought some articles for 900. 5 of them were damaged and the rest were sold for 2 more than what they were bought for for a profit of 80.

Let the number of articles bought initially be X. Each of them cost 900/X.

X - 5 were sold for 900/X + 2 for 980

=> (X - 5)(900/X + 2) = 980

=> 900 + 2X - 4500/X - 10 = 980

=> 2X - 4500/X = 90

=> 2X^2 - 4500 = 90X

=> X^2 - 45X - 2250 = 0

=> X^2 - 75X + 30X - 2250 = 0

=> X(X - 75) + 30(X - 75) = 0

=> (X + 30)(X - 75) = 0

=> X = 75 and X = -30

Ignore the negative root.

The number of articles bought initially was 75.

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