Question

An alloy consists of two metals taken in the ratio $1:2$ and another alloy consists of the same metals taken in the ratio $2:3$. How many parts of the two alloys must be taken to obtain a new alloy consisting of the same metals which are in the ratio $\frac{17}{27}$?

Answer 1

Let say alloy 1 consists of metal $m_1$ and $m_2$ in ratio $1:2$ and alloy 2 consists of metal $m_1$ and $m_2$ in ratio $2:3$.

Now, combining both the alloys to form a new alloy.

So, according to given information $1x+2y=17$ and $2x+3y=27$

Where, $x,y$ represents metal $m_1$ and $m_2$

$⟹2(17-2y)+3y=27⟹y=7$

By replacing $y=7$, we get $x=3$

$⟹$ we need to take first alloy $3$ parts and second alloy $7$ parts