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Question:

Two alloys of aluminium have different percentages of aluminium in them. The first one weighs 8 kg and the second one weighs 16 kg. One piece each of equal weight was cut off from both the alloys and first piece was alloyed with the second alloy and the second piece alloyed with the first one. As a result, the percentage of aluminium became the same in the resulting two new alloys. What was the weight of each cut-off piece?

Explanation:

Let weight of the cut-off piece = X kg

Let percentage of aluminium in 8 kg and 16 kg alloy be a and b respectively.

∴ $\frac{(8 - X) a + X b}{8 \times 100}$ = $\frac{(16 - X) b + X a}{16 \times 100}$

∴ 16a – 2Xa + 2Xb = 16b – Xb + Xa

∴ 16 – 2X = X and 2X = 16 – X

∴ X = $\frac{16}{3}$ = 5.33 kg

Hence, option (c).

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