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?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 4)

Answer 1

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

Now,

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

Required percentage = (23/41) × 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 × Quantity of Alloy P

Ratio in alloy P = 5 : 11

Total quantity = 5 + 11 = 16

So, Total quantity of alloy Q = 3 × 16 = 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 × 6 : 5 × 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 = (23/41) × 100 = 56%

Mistake Points Read the question carefully,

In the last line of the question we have mentioned that,

then aluminum is what percentage of the copper.

Hence we do not have to take the whole weight of the alloy while calculating the % of aluminum.