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प्रश्न
A trader bought a number of articles for Rs. 1,200. Ten were damaged and he sold each of the remaining articles at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction. Taking the number of articles he bought as x, form an equation in x and solve it.
उत्तर
Number of articles bought by the trader = x
It is given that the trader bought the articles for Rs. 1200
So, the cost of one article = Rs. `1200/x`
Ten articles were damaged. So, the number of articles left = x – 10
Selling price of each of (x – 10) articles = Rs. `(x - 10) (1200/x + 2)`
Profit = Rs. 60
`∴ (x - 10)(1200/x + 2) - 1200 = 60`
`1200 + 2x - 12000/x - 20 - 1200 = 60`
`2x - 12000/x - 80 = 0`
2x2 – 80x – 12000 = 0
x2 – 40x – 6000 = 0
x2 – 100x + 60x – 6000 = 0
x(x – 100) + 60(x – 100) = 0
(x – 100)(x + 60) = 0
x = 100, – 60
Number of articles cannot be negative.
So, x = 100.
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