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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 Whole - ICSE Class 10 - Mathematics

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Question

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.

Solution

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

The 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`

`2x^2 - 80x - 12000 = 0` 

`x^2 - 40x - 6000 = 0`

`x^2 - 100x + 60x - 6000 = 0`

x(x - 100) + 60(x - 100) = 0

x = 100, -60

Number of articles cannot be negative. So, x = 100.

 

  Is there an error in this question or solution?

APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6D | Q: 11
Solution 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 Whole Concept: Quadratic Equations.
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