Question

Two alloys of iron have different percentage of iron in them. The first one weighs 6 kg and second one weighs 12 kg. One piece each of equal weight was cut off from both the alloys and the first piece was alloyed with the second alloy and the second piece was alloyed with the first one. As a result, the percentage of iron became the same in the resulting two new alloys. What was the weight of each cut-off piece?

Answer 1

4 kg

Answer 2

how? explain

Answer 3

Suppose the two alloys initially have x% and y% of iron present in them. Let the piece that is being cut from both the alloys be of Z kg. Therefore, the percentage of iron present after mixing the newly cut pieces is same in both the alloys, thus calculating the amount of iron present in each after mixing
In first alloy amount of iron present,
(6 – Z)x/100 + Zy/100
Percentage of iron present in first alloy = ((6 – Z)x/100 + Zy/100) *100
6

In second alloy amount of iron present,
(12 – Z) y/100 + Zx/100
Percentage of iron present in first alloy = ((12 – Z) y/100 + Zx/100) *100
12
Percentage of alloy in the two new alloys are equal, thus

((6 – Z)x/100 + Zy/100) *100 = ((12 – Z) y/100 + Zx/100) *100
6 12
Solving we can get the value of Z = 4 kg

Answer 4

do you get it/