Question

In two types of stainless steel, the ratio of chromium and steel are $2:11$ and $5:21$ respectively. In what proportion should the two types be mixed so that the ratio of chromium to steel in the mixed type becomes $7:32$ ?

• A. $2:3$
• B. $3:4$
• C. $1:2$
• D. $1:3$

Answer 1

The correct option is C $1:2$

Given:

Let the alloys be mixed in the ratio of $x:y$

(Assumption)

In 1st alloy, chromium = $\frac{2x}{13}$

In 1st alloy, steel = $\frac{11x}{13}$

In 2nd alloy, chromium = $\frac{5y}{26}$

In 2nd alloy, steel = $\frac{21y}{26}$

The ratio in which $2$ alloys must be mixed to get a new alloy with a ratio of chromium and steel be $7:32$ =?

Now we have,

$(\frac{2x}{13}+\frac{5y}{26}):(\frac{11x}{13}+\frac{21y}{26})=7:32$

$⟹\frac{(\frac{2x}{13}+\frac{5y}{26})}{(\frac{11x}{13}+\frac{21y}{26})}=\frac{7}{32}$

$⟹\frac{4x+5y}{22x+21y}=\frac{7}{32}$

$⟹128x+160y=154x+147y⟹154x-128x=160y-147y⟹26x=13y⟹\frac{x}{y}=\frac{13}{26}$

$\therefore x:y=1:2$

Therefore the ratio is $1:2$