# How to solve this question on weighted mean?

In one alloy there is 50% steel in its total mass, while in another alloy it is 75%. 15 kg of the first alloy was melted together with 10 kg of the second one to form a third alloy. Find the percentage of steel in the new alloy when it is known that 20% of the total steel is get diminished during the melting process? .

(1) 55% (2) 52% (3) 42% (4) 60% (5) 62%

Doubt:

Is the total weight decreasing Or steel is simply transforming? I would like to have an explanation about the same and also a suggested technique in details is most welcome to solve the problem.

Is the total weight decreasing Or steel is simply transforming?

it is decreasing because simply 20% of total steel mass does not melt... you will have it as a residual.

thus you have

$$\text{ Kg }15\times0.5+\text{ Kg }10\times7.5=\text{ Kg }15$$

Give that 20% of the total steel does not melt you get you loose

$$15\times0.2=\text{Kg }3$$ of total mass thus in the new alloy you get

$$\frac{15-3}{25-3}\approx 55\%$$

• I could not understand what you mean by residual. Oct 5, 2021 at 10:08
• @IshrojarLayok : I tried to interpret the question. I suppose that you loose kg 3 of steel in the new alloy thus you get kg22 of new alloy with kg 12 steel inside and kg3 of steel Oct 5, 2021 at 10:39
• Okay. Thanks but what made you think that way? Oct 5, 2021 at 11:11

If the weight does not diminish, answer is 48% which is not in the option. And, the other way, answer comes out to be nearly 52% which is one of the options. So I suggest you go with that.

However, I think the first way makes more sense as mass doen't simply vanish, more so for steel which has very high boiling point. So according to general knowledge, one should go with 48%. So in case you are not given an MCQ or such answer is part of the choices in the MCQ, then prefer the former case.

Absent the constraint that steel melts, you would have

$$15 + 10 = 25$$ total kg.

Of these $$25$$ kg, you would have
$$[(0.5) \times 15] + [0.75) \times 10] = 15$$ kg of steel.

There are two interpretations that I can think of:

$$\underline{\text{Case 1}}$$
The $$3$$ kg of steel that melts is not to be considered part of the remaining mass.

In this instance, the resulting fraction that is steel is $$\displaystyle \frac{15 - 3}{25 - 3} = \frac{12}{22} = 54.\overline{54}\%$$.

$$\underline{\text{Case 2}}$$
The $$3$$ kg of steel that melts is to be considered part of the remaining mass, that has (somehow been converted) to non-steel.

As I understand it, from a physics point of view, this interpretation seems nonsensical. Melting the steel off is not the same as changing the makeup of the atoms in the steel.

Anyway, under the assumption that the problem composer flunked physics:

In this instance, the resulting fraction that is steel is $$\displaystyle \frac{15 - 3}{25} = \frac{12}{25} = 48\%$$.

• How do you interpret melting of steel? Please explain in details. Oct 5, 2021 at 11:16
• But where would the lost mass go? Oct 5, 2021 at 11:21
• @IshrojarLayok The solid (steel) is turned into either a gas or a liquid, either of which is then separated from the alloy. Presumably, the alloy has a higher melting point than steel, and so remains solid. The (non-sensical) Case 2 scenario, which assumes that the problem composer flunked Physics, likens melting steel, to subjecting it to sub-atomic collisions that change the make-up of the steel atoms to that of the atoms of the alloy. To change one chemical element into another, you must alter the number of protons, neutrons, and electrons in each atom. Oct 5, 2021 at 11:21
• Re previous comment, under Case 1, the melted steel, if a liquid, would be drained off, and if a gas would be sent into the outside world, presumably by a chimney. Actually, I would speculate that the melted steel remains a liquid, kept in a vat, and the (still solid) alloy is lifted out of the vat. Oct 5, 2021 at 11:22
• A new phase which is non solid is formed that is what you mean? Oct 5, 2021 at 11:24