# CAT Practice : Averages, Ratios, Mixtures

Averages

## Averages

Q.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

Choice D. 54 and 75

## Detailed Solution

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)
$(\frac{(72 + x)}{7})x - 3x = 810$
= ) 72x + x2 – 21x = 810 x 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.

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