Question

P and Q are two alloys of aluminum and copper. The ratios of aluminum 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 aluminum is what percentage (rounded off to the nearest integer) of the copper in the third alloy?

• A. 63 Percent
• B. 52 Percent
• C. 48 Percent
• D. 56 Percent

Answer 1

Answer:

D. 56 Percent

Given:

The ratios of aluminum and copper in P (Al : Cu) = 5 : 11

The ratios of aluminum and copper in Q (Al : Cu) = 3 : 5

Calculation:

The ratio of P is 5 : 11, a total of 16

The ratio of Q is 3 : 5, a total of 8

Now multiply the second ratio by  2 to make the quantity equal.

The ratio of Q is 6 : 10, a total 16

If a third alloy is formed by mixing alloys P and Q in the ratio of 1 ∶ 3.

Now multiply the first ratio by 1 and the second ratio by 3, as the third alloy is formed by mixing in 1 : 3 ratio

	Al	Cu
P	$5\times{1}=5$	$11\times{1}=11$
Q	$6\times{3}=18$	$10\times{3}=30$

Now,

The final ratio in third alloy Al : Cu = 23 : 41

Required percentage = $\frac{23}{41}\times{100}$= 56.09 ≈ 56%

∴ The correct answer is 56%.

Alternate Method

According to the question, 

In the third alloy, P : Q ​= 1 : 3

⇒ Quantity of alloy Q = $3\times$Quantity of Alloy P

Ratio in alloy P = 5 : 11 

Total quantity = 5 + 11 = 16

So, Total quantity of alloy Q = $3\times{6}$ = 48

But, Ratio of Alloy Q = 3 : 5, means total quantity = 3 + 5 = 8

To make it 48, we multiply the ratio of Q by 6

Then, Ratio of Q = $3\times{6}$ : $5\times{6}$

Ratio of Alloy Q = 18 : 30

Now, the ratio of P and Q becomes in the ratio 1 : 3.

Now, After mixing both the alloys, the ratio will be 

Aluminium :  Copper = (5 + 18) : (11 + 30) = 23 : 41

so, Aluminium% w.r.t. Copper = $\frac{23}{41}\times{100}$ = 56%