das.ashmita wrote:
Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2, respectively. A new alloy T is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy T ?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 4 : 3
(E) 7 : 9
Amount of element 1 :
In first alloy: 5/8
In second alloy: 1/3
In alloy T: 4/7
Unlike the first two fractions -- which indicate (element 1)/total -- the fraction in red = (alloy A)/total.
Here is the distinction:
In the X and Y problem, alligation was used to determine the ratio of the two ingredients being combined (X and Y).
In the alloy problem, we are GIVEN the ratio of the two ingredients being combined:
A:B = 4:3.
Our job is to determine the composition of alloy T with regard to the TWO ELEMENTS.
Here is how alligation could be used:
Let A = the fraction of element 1 in alloy A.
Let B = the fraction of element 1 in alloy B.
Let T = the fraction of element 1 in alloy T.
Step 1: Convert to FRACTIONS the ratios attributed to the two INGREDIENTS.
A:
Since (element 1) : (element 2) = 5:3, (element 1)/total = 5/8.
B:
Since (element 1) : (element 2) = 1:2, (element 1)/total = 1/3.
Step 2: Put these fractions over a COMMON DENOMINATOR.
A = 5/8 = 15/24.
B = 1/3 = 8/24.
Step 3: Plot the 2 fractions at the ends of a number line, with the unknown goal fraction (T) in the middle.
A(15/24)----------------T--------------------B(8/24)
Step 4: The distances between the fractions = the RECIPROCAL of the ratio of A:B in the mixture.
A(15/24)-------
3x-------T---------
4x---------B(8/24)
Step 5: Solve for x.
Since the total distance between 15/24 and 8/24 = 7x, we get:
x = (15/24 - 8/24)/7 = 1/24.
Step 6: Calculate the value of the goal fraction.
T = 15/24 - 3x = 15/24 - 3(1/24) = 12/24 = 1/2.
Since element 1 = 1/2 of alloy T, (element 1) : (element 2) = 1:1.
The correct answer is
A.
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