TANCET 2023 Solved Papers

Concept:The given new ratio $15:9:6$ simplifies to $5:3:2$, which is exactly the same as the original ratio of the alloy. Hence, no change in iron is actually needed.Explanation:Let the initial quantities of Zinc, Lead, and Iron be $5x$, $3x$, and $2x$ respectively.Total mass is given as:$5x + 3x + 2x = 150$$\Rightarrow 10x = 150$$\Rightarrow x = 15$So the present masses are:Zinc $= 5 \times 15 = 75$ kgLead $= 3 \times 15 = 45$ kgIron $= 2 \times 15 = 30$ kgNow, suppose $y$ kg of iron is added. Then the new amount of iron becomes $30 + y$ kg.For the alloy to have the ratio $15:9:6$, compare the amounts of Zinc and Iron.$\frac{75}{30 + y} = \frac{15}{6}$$\Rightarrow \frac{75}{30 + y} = \frac{5}{2}$$\Rightarrow 150 = 150 + 5y$$\Rightarrow y = 0$Therefore, no iron needs to be added to 150 kg of this alloy.Since $0$ kg is not present among the given options, none of the provided choices is correct.Answer:$0$ kg; none of the given options is correct.