CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

The question is from CAT Ratio, Mixtures and Averages. All we need to do is, forming the equation as per the question and substituting the options in that to get the answer. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023.

Question 43: For a global sports event, Nike has to make 810 pair of shoes while Adidas has to make 900 pair of shoes, in the same period of time. Nike could complete the order 3 days before the scheduled time while Adidas completed the order 3 days before Nike. How many pair of shoes did each make per day if Adidas made 21 more shoes per day than Nike?

1. 44 and 65
2. 21 and 42
3. 34 and 55
4. 54 and 75

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: How the individual data points affect the average?

Let Nike make x pair of Shoes/day
So, Adidas makes (x + 21) pair of Shoes/day
Also, let the schedule delivery be in Y number of days.
Therefore,
x(y-3) = 810
=> xy – 3x = 810………………….(1)
and, (x+21) (y-6) = 900
=> xy + 21y – 6x -126 = 900
Putting xy from (1)
=> 810 + 3x + 21y – 6x = 1026
=> 21y – 3x = 216
=> y = \\frac{(72 + x)}{7}\\)
Putting y in equation (1) (Sometimes, you just gotta solve)
\\frac{(72 + x)* x}{7}\\) - 3x = 810
=> 72x + x² – 21x = 810 * 7
=> x² + 51x – 5670 = 0
From the looks of the equation, x has to be a large number. Start by putting the largest number in equation x = 54 satisfies the equation.

The question is "How many pair of shoes did each make per day if Adidas made 21 more shoes per day than Nike?"

Hence, the answer is "54 and 75".

Choice D is the correct answer.