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 = ?

Answer: Option C

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,
$$\begin{array}{rl}& \left(\frac{2x}{13}+\frac{5y}{26}\right):\left(\frac{11x}{13}+\frac{21y}{26}\right)=7:32\\ & \Rightarrow \frac{\left(\frac{2x}{13}+\frac{5y}{26}\right)}{\left(\frac{11x}{13}+\frac{21y}{26}\right)}=\frac{7}{32}\\ & \Rightarrow \frac{\frac{4x+5y}{26}}{\frac{22x+21y}{26}}=\frac{7}{32}\\ & \Rightarrow \frac{4x+5y}{22x+21y}=\frac{7}{32}\\ & \Rightarrow 128x+160y=154x+147y\\ & \Rightarrow 154x-128x=160y-147y\\ & \Rightarrow 26x=13y\\ & \Rightarrow \frac{x}{y}=\frac{13}{26}\\ & \therefore \frac{x}{y}=\frac{1}{2}\end{array}$$

∴ Ratio in which 2 alloys must be mixed to get a new alloy with a ratio of chromium and Steel to be 7 : 32 is 1 : 2