Question : P and Q are two alloys of Aluminium and Copper. The ratios of Aluminium and Copper in P and Q are 5 : 11 and 3 : 5, respectively. If a third alloy is formed by mixing alloys P and Q in the ratio of 1 : 3, then Aluminium is what percentage (rounded off to the nearest integer) of the Copper in the third alloy?
Option 1: 63%
Option 2: 52%
Option 3: 48%
Option 4: 56%
Correct Answer: 56%
Solution :
In the case of P :
Ratio = 5 : 11
Total = 5 + 11 = 16 units
In the case of Q :
Ratio = 3 : 5
Total = 3 + 5 = 8 units
Now, a third alloy is formed by mixing alloys P and Q in the ratio of 1 : 3. So, 16 units of alloy P and 48 units of alloy Q should be taken.
So, ratio of Aluminium to Copper in third alloy = (5 + 6 × 3) : (11 + 6 × 5)
= 23 : 41
Required percentage = $\frac{23}{41}\times 100 = 56$%
Hence, the correct answer is 56%.
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