Problem Solving

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

Let the actual amount of A be 4x and actual amount of B be 3x since A and B are in the ratio 4/3

amount of first basic element in the new alloy T (5/8)*4x + (1/3)*3x = (7x)/2

amount of second basic element in the new alloy T (3/8)*4x + (2/3)*3x= (7x)/2

so ratio of first basic element to second basic element: [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1 ( Answer A)

Courtesy @ Anurag BTG

This sum has been solved using the Method described by Anurag in this link
https://www.beatthegmat.com/two-mixtures ... tml#485113

gmatter2012 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

Let F = the first element and S = the second element.

Alloy A:
Since F:S = 5:3, and 5+3=8, F/total = 5/8.

Alloy B:
Since F:S = 1:2, and 1+2 = 3, F/total = 1/3.

Mixture T:
A:B = 4:3.
If we mix 8 units of A with 6 units of B, we get:
Amount of F in alloy A = (5/8)8 = 5 units
Amount of F in alloy B = (1/3)6 = 2 units.
(Total F)/(Mixture T) = (5+2)/(8+6) = 7/14 = 1/2.
Since 1/2 of the mixture is composed of F, F:S = 1:1.

The correct answer is A.

Hi GMATGuruNY

I tried solving this question with alligation approach you have mentioned in the thread below.
https://www.beatthegmat.com/two-mixtures ... tml#485113

And i am getting the ans as 9:40. can you please point out the mistake.

Amount of element 1 :
In first alloy: 5/8
In second alloy: 1/3
In alloy T: 4/7

therefore, by alligation:

5/8-4/7 : 4/7-1/3
3/56 : 5/21
9:40

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.

Thanks a lot Mitch.
I had misinterpreted the information in the question.

The ratio of elements in two alloys are 5:3 and 1:2.
Let the weight of 1unit of each alloy be 8 x 3 = 24.
Then alloy A will have elements weighing 15 and 9.
Alloy B will have elements weighing 8 and 16.
Now these two alloys are mixed in the ratio 4:3.
So, weight of elements taken from alloy A = 60 and 36.
Weight of elements taken from alloy B = 24 and 48.
Ration of elements in final alloy = (60+24)/(36+48) = 1:1.
Hence, A is the answer.