Question

Two alloys are both made up of copper and tin. the ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. in what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3

Answer 1

Given:
⇔ Let the alloys be mixed in the ratio of X : Y (Assumption)
⇔ In 1st alloy, Copper = x/4
⇔ In 1st alloy, Tin = 3x/4
⇔ In 2nd alloy, Copper = 2y/7
⇔ In 2nd alloy, Tin = 5y/7

To find:
⇔ Ratio in which 2 alloys must be mixed to get a new alloy with ratio of copper and tin be 3 : 8 = ?

Solution:
⇔ Now we have, 
⇒ (x/4 + 2y/7) : (3x/4 + 5y/7) = 3 : 8
⇒ (x/4 + 2y/7) / (3x/4+ 5y/7) = 3/8
⇒ (7x + 8y/28) / (21x + 20y/28) = 3/8
⇒ (7x + 8y) / (21x + 20y) = 3/8
⇒ 8 (7x + 8y) = 3 (21x + 20y)
⇒ 56x + 64y = 63x + 60y
⇒ 64y - 60y = 63x - 56x
⇒ 4y = 7x
⇒ ∴x/y = 4/7

⇒ Ratio in which 2 alloys must be mixed to get a new alloy with ratio of copper and tin be 3 : 8 = 4/7

:)