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A merchant decides to sell off 100 articles a week at a selling price of Rs. 150 each. For each 4% rise in the selling price he sells 3 less articles a week. If the selling price of each article is Rs x, then which of the below expression represents the rupees a week the merchant will receive from the sales of the articles?
1. 175 - x/2
2. x/3 + 156
3. 350 - x2/2
4. x2 - 2x + 75

Choice A. 175 - x/2

Detailed Solution

The selling price per article is Rs. x
The price of the article is Rs (x - 150) more than Rs 150

4% rise from Rs 150 ==> Rs 6
For each Rs 6 increase in price over Rs.150, he sells 3 articles lesser.

So, the reduction in number of articles = (x – 150) / 6 * 3
So, in the new price of Rs.x he sells 100 - (x – 150) / 6 * 3
Or he sells 100 – (x – 150)/2
= (200 – x + 150) / 2
= (350 – x)/ 2
= 175 – x/2

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