Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
Two alloys contain zinc and copper in the ratio of 2 : 1 and 4 : 1. In what ratio the two alloys should be added together to get a new alloy having zinc and copper in the ratio of 3 : 1?
(a)3 : 5
(b)5 : 7
(c)7 : 5
(d)None of these
Answer
Answer (as printed): A
Explanation
Zinc in first alloy $= \frac{2}{3}$ units; Zinc in second alloy $= \frac{4}{5}$ units. Copper in first alloy $= \frac{1}{3}$ units; Copper in second alloy $= \frac{1}{5}$ units. Let the first and second alloys be mixed in the ratio $1 : y$. Then, $$\frac{\frac{2}{3}+\frac{4y}{5}}{\frac{1}{3}+\frac{y}{5}} = \frac{3}{1} \Rightarrow 10+12y = 3(5+3y) \Rightarrow 10+12y = 15+9y \Rightarrow 3y = 5 \Rightarrow y = \frac{5}{3}.$$ $\therefore$ Required ratio $= 1 : \frac{5}{3} = 3 : 5$.
Explanation as extracted from the printed page; notation may be imperfect.