SSC CGL (Prelims) General: Percentage and Mixture questions with solutions

Q1. An alloy contains zinc and copper in the ratio 3:2. A second alloy contains zinc and copper in the ratio 4:1. What quantity of the first alloy must be mixed with 15 kg of the second alloy to produce a new alloy with zinc and copper in the ratio 13:7?

1. 25 kg
2. 35 kg
3. 45 kg
4. 50 kg

Answer: 45 kg

First alloy has zinc fraction 3/5 and copper fraction 2/5. Second alloy has zinc fraction 4/5 and copper fraction 1/5, and the final mixture must have zinc fraction 13/20. Let x kg be the first alloy. Then \(\frac{3x}{5}+12 = \frac{13}{20}(x+15)\), which gives x = 45.