Question

Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

• A. $1:1$
• B. $1:2$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is D $3:2$

Let weight of Gold be 19k and that of copper be 9k.

Let the percentage of Gold in alloy be p and of copper be 1-p.

So

$19k\times p+9k\times (1-p)=15k$

$19p+9(1-p)=15$

$19p-9p+9=15$

$10p=6$

$p=\frac{6}{10}$

$p=\frac{3}{5}$

$1-p=1-\frac{3}{5}=\frac{2}{5}$

ratio$=\frac{p}{1-p}=\frac{\frac{3}{5}}{\frac{2}{5}}$

ratio$=\frac{3}{2}$

Hence the correct option is (D).