A bag containing 60 balls consists of red balls and blue balls only.

Question

A bag containing 60 balls consists of red balls and blue balls only. The number of red balls are at least 60% of the number of blue balls, and there is at least one ball of each color.

Select for Maximum Red the maximum possible number of red balls and select for Maximum Blue the maximum possible number of blue balls. Make two selections only, one in each column.

chetan2u · Accepted Answer

R + B = 60 and  R\geq 0.6B

Maximum red:   The number of red balls are at least 60% of the number of blue balls, and there is at least one ball of each color. 
 Thus, there is a lower restriction to the numbers of red ball, but no upper restriction, except that there is one blue ball for sure.  
  Hence, the Maximum numbers of red ball is 60-1 or 59 balls.

Maximum Blue:  
From the equation above least number of red balls = 0.6B. Hence 0.6B + B =60 or 1.6B = 60 or  B = \frac{60}{1.6} = 37.5 .
 Now, comes the dilemma: whether to take it as 37 or 38. 
Remember the red balls are at least 60% of blue balls, and we get the least value of red as 60-37.5 or 22.5 balls. So  R \geq 22.5 ,   and the lowest possible integer value is 23, making Blue balls 60-23 or 37.

Saloni_such  I hope it clears your doubt.

Saloni_such · Answer

Please give an explanation why it is 37 and not 38

thisischelso · Answer

A bag containing 60 balls consists of red balls and blue balls only. The number of red balls are at least 60% of the number of blue balls, and there is at least one ball of each color.

Select for Maximum Red the maximum possible number of red balls and select for Maximum Blue the maximum possible number of blue balls. Make two selections only, one in each column.

------------

This is a min max question. From the question stem, you know that

Total = 60 = # of Red + # of Blue 
# of Blue = X 
# of Red is greater than or equal to 0.6 X.

For Scenario 1: Maximum Red. You know that at least 1 ball of each color exists. So we should assume the following
- At least 1 blue ball exists 
- Some number of red balls. Since there aren't any upper level constraints on how many Red balls exist, that means that there could be up to 59 Red Balls.

For Scenario 2: Lets assume that the # of Red balls is 0.6X. That implies that

X + 0.6X = Total balls = 60 
1.6X = 60 
X = 37.5

But remember that we're counting number of objects. There is no way to have 0.5 of a ball. So we should round DOWN to the nearest integer. Thus, there is a maximum of 37 blue balls.

Dooperman · Answer

If X= No of Red balls & Y= No of Blue Balls. 
X= 60 - Y

X ≥ 60% (60 - X). Given in statement.
X ≥ 22.5 (Thus Xmin = 23)

60 - Y ≥ 22.6

Y ≤ 37.5 (Thus Ymax = 37. Since X&Y are integers).

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A bag containing 60 balls consists of red balls and blue balls only.

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