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Moderate Problems on Mixture

Below are three problems based on the concept of mixtures in some ratio.
Question 1
A certain box of health drink powder is obtained by mixing the makers as 3 parts of milk powder with 5 parts of energy powder. If 2 kg of the mixture is needed and the individual makers can be purchased only in one kg or half kg box. What is the least amount of makers, in kg's, that must be purchased in order to measure out the portions needed for the mixture?
a)2kg b)3kg c)4.5kg d)2.5kg
Answer : d)2.5kg
Solution :
Step 1) "A certain box of health drink powder is obtained by mixing the makers as 3 parts of milk powder with 5 parts of energy powder. "
You should think: 3 parts of milk powder, 5 parts of energy powder sums to a total of 8 parts.
More specifically, 3/8 of the mixture is milk powder and 5/8 of the mixture is energy powder.
Step 2) "If 2 kgs of the mixture is needed and the individual makers can be purchased only in one kg or half kg cans"
So we know the mixture is 2 kg. How much of these 2 kg is milk powder and how much of these 2 kg is energy powder?
We know 3/8 of the mixture is milk powder. And the entire mixture is 2 kg.
So 3/8 of the 2 kg = 3/8 x 2 = 6/8 = 3/4 = .75 of a kg is milk powder
Likewise 5/8 of the 2 kg or 5/8 x 2 = 10/8 = 5/4 = 1.25 of the kg is energy powder
Step 3) " individual makers can purchase only in one-kg or half- kg cans"
That means the .75 needs to be rounded up to 1 kg
And it means that the 1.25 kg needs to be rounded up to 1.5 kgs (a 1 kg box and a half kg box)
Combine the 1 kg of milk powder + 1.5 kg of energy powder = 2.5 total kgs.
Hence the answer is option d.
Question 2
A certain shade of orange color is obtained by mixing 1 part of white color with 2 parts of red color. If 3.6 kgs of the mixture is needed and the white and red colors can be purchased only in 1 kg, what is the least amount of color, in kg's, that must be purchased for the mixture?
a)5kg b)4kg c)6kg d)4.5kg
Answer : a)5kg
Solution :
Since, the orange color is obtained by mixing 1 part of white color with 2 parts of red color.
i.e., 1 part white color, 2 part red color, that means totally there are 3 parts.
Then, 1/3 of the mixture is white color and 2/3 is red color.
Given that, 3.6 kg of the mixture is needed.
We know 1/3 of the mixture is white color and the entire mixture is 3.6 kg
So 1/3 of 3.6 kg = 3.6/3 = 1.2 kg is white color.
Likewise 2/3 of the 3.6 kg = 2 x 3.6/3 = 2 x 1.2 = 2.4 kg is red color.
Since the individual colors (white and red) can be purchased only in one-kg
i.e., 1.2 kg needs to be rounded up to 2 kg
And 2.4 kg needs to be rounded up to 3 kg.
Combine the white and red color = 2kg + 3kg = 5 kg.
Hence the least amount of colors to be purchased is 5 kg.
Question 3
A certain shade of violet color is obtained by mixing 2 parts of white color with 3 parts of blue color. If 8 kg of the mixture(violet color) is needed and the individual colors can be purchased only in 2 kg cans worth Rs.80, then what is the least amount of color in kg's that must be purchased for the mixture? And how much rupees spend to purchase the blue color cans?
a)6kg & Rs.480 b)10kg & Rs.400 c)10kg & Rs.800 d)6kg & Rs.320
Answer : b)10kg & Rs.400
Solution :
Since the violet color is obtained by mixing 2 parts of white color with 3 parts of blue color.
i.e., 2 parts of white color and 3 parts of blue color, that means totally there are 5 parts.
Then, 2/5 of the violet color is white and 3/5 is blue color.
Given that, 8kg of the mixture is needed.
So 2/5 of 8kg = 2 x 8/5 = 3.2 kg is white color
Likewise 3/5 of 8kg = 3 x 8/5 = 4.8 kg is blue color.
Since the individual colors (white and red) can be purchased only in 2-kg cans.
i.e., 3.2 kg needs to be rounded up to 4 kg.
And 4.8 kg needs to be rounded up to 6 kg.
Then the required least amount of colors = 4kg + 6kg = 10kg or 5 cans (2 cans of white + 3 cans of blue)
Since each can of 2 kg color worth Rs.80. Total cost for 5 cans = 5 x 80 = Rs. 400
Hence the answer is 10kg & Rs.400.

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