CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

The question is about Linear Equations and Profit and Loss. This is an application based question which is based on linear equation. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 17: 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 number of articles sold by the merchant in that week?

1. 175 - \\frac{x}{2}\\)
2. \\frac{x}{3}\\) + 156
3. 350 - \\frac{x^2}{2}\\)
4. x² - 2x + 75

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Quadratic Equations: An application based question!

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 = (\\frac{(x – 150)}{6}\\)) * 3
So, in the new price of Rs.x he sells 100 - (\\frac{(x – 150)}{6}\\)) * 3
Or he sells 100 – \\frac{(x – 150)}{2}\\)
= \\frac{(200 – x + 150)}{2}\\)
= \\frac{(350 – x)}{2}\\)
= 175 – \\frac{x}{2}\\)

The question is "If the selling price of each article is Rs x, then which of the below expression represents the number of articles sold by the merchant in that week?"

Hence the answer is "175 - \\frac{x}{2}\\)"

Choice A is the correct answer.