ratio and proportion

Two alloys A and B are composed of two basic elements p and q. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X 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 X?

Answer:

Basis:

1 kg of Alloy A and 1 kg of alloy B

Let the elements in the alloy be “p” and “q”

So, in A,

p = 5/8 kg, q = 3/8 kg

So, in B,

p = 1/3 kg, q = 2/3 kg

In the new alloy X there is 4 kgs of A and 3 kgs of B

So, p = 4 x (5/8) + 3 x (1/3) = (20/8) + 1 = 7/2 kg

So, q = 4 x (3/8) + 3 x (2/3) = 7/2 kg

So, ratio of p and q in X = (7/2) : (7/2) = 1: 1 Answer