21. A mixture "M1" of Mix Juice, Orange Juice and Pineapple Juice contains 90% Mix Juice, 5% Orange Juice and 5% Pineapple Juice. A second mixture "M2" of Mix Juice and Orange Juice is mixed with M1 such that the resulting mixture "M3" contains 85% of Mix Juice, 12.5% of Orange Juice, and 2.5% Pineapple Juice. What is the ratio of percentage of Orange Juice in M2 to the percentage of Mix Juice in M1?
Answers
A line is missing in the question :
Both Mixtures M1 & M2 are mixed in equal quantities
Consider 100ml of Mixture M1 is taken.
So, It contains
90 ml Mix Juice
5 ml Pine apple juice
5 ml Orange juice.
100 ml of Mixture M2 is taken,
It contains
x ml of Mix Juice
(100 - x) ml of Orange Juice
M3 mixture is formed by Mixing M2 & M1.
200 ml of Mixture M3 is formed.
Given, It contains
85% of Mix Juice, 12.5% of Orange Juice, and 2.5% Pineapple
Amount of Mix Juice = 85% of 200 ml = 170 ml.
170 ml of Mix Juice of M3 is formed by adding 90 ml of Mix Juice from M1 & x ml of Mix Juice from M2
170 = 90 + x
x = 80 ml.
Therefore, M2 contains 80 ml of Mix Juice
Amount of Orange Juice in M2 = 100 - 80 = 20 ml.
Percentage of Mix Juice in M1 = 90 % ( Given)
Percentage of Mix Juice in M2 = 20%
The ratio of percentage of Orange Juice in M2 to the percentage of Mix Juice in M1 = 20 : 90 = 2 : 9.
Else, We can also prove that M1 & M2 are equal from the data.
For M1,
Orange Juice = 0.05 M1 ( 5% of M1 in other words is 0.05 M1)
Mix Juice = 0.9 M1
Pine Apple Juice = 0.05 M1
For M2,
Mix Juice = xM1
Then Orange juice is( 1 - x) M1
For M3,
Mix Juice = 0.85 M3 = 0.9M1 + ( 1 - x) M1
Orange Juice = 0.125 M3 = 0.05 M1 + ( 1- x) M1
Pine Apple Juice = 0.025 M3 = 0.05 M1
But We know M3 is formed by Mixture of M1 & M2
We can write,
0.025 ( M1 + M2) = 0.05 M1
0.025 M1 = 0.025 M2
This tells us that M1, M2 are in equal quantities.
Answer:
2: 9
Step-by-step explanation:
A mixture "M1" of Mix Juice, Orange Juice and Pineapple Juice contains 90% Mix Juice, 5% Orange Juice and 5% Pineapple Juice
=> Mix juice = 0.9M1
Orange Juice = 0.05M1
Pineapple Juice = 0.05M1
A second mixture "M2" of Mix Juice and Orange Juice is mixed
=> Orange Juice = M1 * O
Mix Juice = 1 - M1 * O
Total Mixture M3 = M1 + M2
Mix Juice = 0.85M3 = 0.85(M1 + M2) = 0.9M1 + (1 - M1* O)
Orange Juice = 0.125M3 = 0.125(M1 + M2) = 0.05M1 + M1 * O
Pineapple juice = 0.025M3 = 0.025(M1 + M2) = 0.05M1
=> 0.025(M1 + M2) = 0.05M1
=> M2 = M1
=> 0.125(M1 + M1) = 0.05M1 + M1 * O
=> M1* O = 0.2M1
=> O = 0.2
=> Orange percentage in M2 = 20 %
Mix Juice Percentage in M1 = 90%
=> 20 : 90
=> 2: 9