Question

Two alloys A and B contain gold and copper in the ratios of $2:3$ and $3:7$ by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is

• A.
  $5:10$
• B.
  $7:13$
• C.
  $6:11$
• D.
  $9:13$

Answer 1

The correct option is B

$7:13$
Alloy A contains Gold and Copper.

Let 2x:3x

Which is same as 4x:6x

Alloy B contains Copper 3x:7x

As masses of Alloy A is equal to Alloy of mass B.
i.e

Gold Copper

i.e $Alloy14x:6x\Rightarrow 10x\left(mass\right)$
$Alloy23x:7x\Rightarrow 10x\left(mass\right)$

$\therefore \text{Ratio of Gold to Copper is}$

$\frac{\text{Gold from alloy 1 + Gold of alloy 2}}{\text{Copper from alloy 1 + Copper of alloy 2}}$

$=\frac{4x+3x}{6x+7x}=\frac{7x}{13x}=\frac{7}{13}$