In an alloy (A), zinc and copper are in the ratio 1 ∶ 2. In the second alloy (B). zinc and copper are in the ratio 2 ∶ 3. In what ratio should these two alloys A and B be mixed to form a new alloy in which the ratio of copper and zinc is 8 ∶ 5?

In an alloy (A), zinc and copper are in the ratio 1 ∶ 2. In the second alloy (B). zinc and copper are in the ratio 2 ∶ 3. In what ratio should these two alloys A and B be mixed to form a new alloy in which the ratio of copper and zinc is 8 ∶ 5? Correct Answer 3 ∶ 10

Let the mixture be mixed in the ratio of A ∶ B.

First mixture zinc and copper = A/3 and 2A/3

Second mixture zinc and copper = 2B/5 and 3B/5

Ratio of mixture = 5 ∶ 8

Then,

⇒ (A/3 + 2B/5) ∶ (2A/3 + 3B/5) = 5 ∶ 8

⇒ 8A/3 + 16B/5 = 10A/3 + 15B/5

⇒ 40A + 48B = 50A + 45B

⇒ 10A = 3B

⇒ A /B = 3 /10