guerrero wrote:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 14 liters of drink A to convert it to drink B ?
a) 4
b) 2/3
c) 3.5
d) 3
e) 4.67
Here's how to solve with ALLIGATION.
Let J = the pure fruit juice to be added to A.
Milk/total in A = 4/7.
Milk/total in J = 0.
Milk/total in B = 3/7.
Step 1: Plot the 3 fractions on a number line, with the fractions attributed to A and J (4/7 and 0) on the ends and the goal fraction (3/7) in the middle.
A(4/7)----------3/7-----------J(0)
Step 2: Calculate the distances between the fractions.
A(4/7)---
1/7----3/7----
3/7----J(0)
Step 3: Determine the ratio in the mixture.
The required ratio of A to J is the RECIPROCAL of the distances in red.
A : J = 3/7 : 1/7 = 3:1.
Since the actual amount of A is 14 liters, both parts of the ratio above must be multiplied by 14/3:
A : J = (14/3 * 3) : (14/3 * 1) = 14 : 14/3.
Thus, J = 14/3.
The correct answer is
E.
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