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 ?
Answer & explanation
Correct answer: option 4
Ratio in P;
Al : Cu = 5 : 11 = (5 + 11) = 16 units,
Ratio in Q,
Al : Cu = 3 : 5 = (3 + 5) = 8 units,
To make unit equal we multiply Q with 2,
Therefore new ratio of Q,
Al : Cu = 6 : 10,
⇒ Now the third Alloy is formed by mixing P and Q in ratio 1 : 3.
Now multiplying P ratio with 1 and Q with 2,
So, Final ratio of third alloy = Al : Cu = 23 : 41,
Required percentage = \(\frac{23}{41}\) x 100 = 56.09 = 56%