An alloy contains tin and copper in the ratio 5 : 3. A second alloy contains tin and copper in the ratio 3 : 1. What quantity of the first alloy must be mixed with 20 kg of the second alloy to produce a new alloy with tin and copper in the ratio 4 : 2?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 40 kg.
Alloy1: Tin = 5/8, Copper = 3/8
Alloy2: Tin = 3/4, Copper = 1/4
Let x kg of alloy1 mixed with 20 kg of alloy2.
Total tin = (5/8)x + (3/4) × 20 = (5x/8) + 15
Total copper = (3/8)x + (1/4) × 20 = (3x/8) + 5
Final ratio of tin and copper = 4 : 2 = 2 : 1
(5x/8 + 15)/(3x/8 + 5) = 2/1
⇒ 5x/8 + 15 = 2(3x/8 + 5) = 6x/8 + 10
⇒ 5x + 120 = 6x + 80
⇒ x = 40 kg