question_answer

In an alloy, zinc and copper are in the ratio 1: 2. In the second alloy, the same elements are in the ratio 2: 3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5 : 8, the ratio of these two alloys in the new alloys is

A) 3 : 10   

B) 3: 7

C) 10: 3    

D) 7: 3

Correct Answer: A

Solution :

In first alloy, zinc \[=\frac{1}{3}\] In second alloy, zinc \[=\frac{2}{5}\] In the new alloy, zinc \[=\frac{5}{13}\] By the rule of Alligation,             \[\therefore \] Required ratio \[=\left( \frac{2}{5}-\frac{5}{13} \right):\left( \frac{5}{13}-\frac{1}{3} \right)\]                         \[=\frac{26-25}{65}:\frac{15-13}{39}\]                         \[=\frac{1}{65}:\frac{2}{39}=\frac{1}{5}:\frac{2}{3}=3:10\]