An alloy P has copper and zinc in the proportion of 5:2 (by weight), while another alloy Q has the same metals in the proportion of 3:4 (by weight). If these two alloys are mixed in the proportion of a:b (by weight), a new alloy R is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy S, formed by mixing the two alloys P and Q in the proportion of b:a (by weight), is

An alloy P has copper and zinc in the proportion of 5:2 (by weight), while another alloy Q has the same metals in the proportion of 3:4 (by weight).

Alloy P and Alloy Q are mixed in the ratio a:b to form alloy R. Let us assume the amount of alloy P is 7a, and the amount of alloy Q is 7b. 

The amount of Copper and Zinc in alloy P will be 5a and 2a, respectively. The amount of Copper and Zinc in alloy Q will be 3b and 4b, respectively. Thus, in alloy R, the amount of Copper and Zinc will be 5a+3b and 2a+4b, respectively. And it is given that alloy R has equal contents of copper and zinc.

=> 5a + 3b = 2a + 4b => b = 3a => a:b = 1:3.

Now, alloy S is formed by mixing the two alloys P and Q in the proportion of b:a. That is, they are mixed in a 3:1 ratio. Let us assume the amount of alloy P as 21x, and the amount of alloy Q as 7x.

The amount of Copper and Zinc in alloy P will be 15x and 6x, respectively. The amount of Copper and Zinc in alloy Q will be 3x and 4x, respectively. Thus, in alloy S, the amount of Copper and Zinc will be 15x + 3x = 18x and 6x + 4x = 10x, respectively.

Thus, the proportion of copper and zinc in the alloy S will be 18x:10x = 9:5.