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I was preparing for Quantitative aptitude exams and I came across this question of ratios

An alloy contains copper and zinc in ratio 5:2 and another alloy contains zinc and tin in the ratio 3:2. If 2 parts of 1st alloy and one part of second alloy are melted together to form a new alloy of copper, zinc and tin, the ration of the metals will be?

What I've understood is that 2 parts of 1st ratio(lets call it A) means 2*A=10:4 and 1 part of the second ratio(lets call it B) means 1*B=3:2. Now when these parts are melted together the ratios will be copper:zince:tin=10:4+3:2 Did I get this right or not?

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  • $\begingroup$ The ratio will be $\frac 2 3 \times \frac 5 7 : (\frac 2 3 \times \frac 2 7 + \frac 1 3 \times \frac 3 5) : \frac 1 3 \times \frac 2 5.$ $\endgroup$ – Dbchatto67 Apr 19 at 10:20
  • $\begingroup$ the question had following 4 choices a)5:5:4 b)10:7:4 c)5:6:4 d)10:7:8 $\endgroup$ – Prime Apr 19 at 10:25
  • $\begingroup$ @Dbchatto67 won't it be $\frac{2}{3}\times\frac{5}{7}:\frac{2}{3}\times\frac{2}{7} + \frac{1}{3}\times\frac{3}{5}:\frac{1}{3}\times\frac{2}{5}$ $\endgroup$ – Vizag Apr 19 at 10:26
  • $\begingroup$ I have done exactly that @Vizag.I first think the two alloys are mixed in the ratio $1:1.$ $\endgroup$ – Dbchatto67 Apr 19 at 10:29
  • $\begingroup$ The ratio will be $$\frac 2 3 \times \frac 5 7 : \left (\frac 2 3 \times \frac 2 7 + \frac 1 3 \times \frac 3 5 \right ) : \frac 1 3 \times \frac 2 5 = \frac {10} {21} : \frac {41} {105} : \frac {2} {15} =50:41:14.$$ $\endgroup$ – Dbchatto67 Apr 19 at 10:30
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So $A_1$ has the following composition:

$$\frac{5}{7} \text{ Cu, } \frac{2}{7} \text{ Zn } $$

$A_2$ has the following composition:

$$\frac{3}{5} \text{ Zn, } \frac{2}{5} \text{ Pb } $$

Now when they are mixed in the ratio $2:1$, the overall mixture will have Cu:Zn:Pb in the ratio :

$$ \frac{2}{3}\times\frac{5}{7}:\frac{2}{3}\times\frac{2}{7} + \frac{1}{3}\times\frac{3}{5}:\frac{1}{3}\times\frac{2}{5}$$

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  • $\begingroup$ the question had following 4 choices a)5:5:4 b)10:7:4 c)5:6:4 d)10:7:8 is it possible that we're doing something wrong related to 2 parts and 1 parts thing? $\endgroup$ – Prime Apr 19 at 10:46
  • $\begingroup$ There surely is a problem with those options. The approach is correct. $\endgroup$ – Vizag Apr 19 at 10:50

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