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Amal preparing an alloy by mixing the other two alloys. The first alloy contains zinc and carbon in the ratio of 1 : 3 and the second alloy contains Aluminium and zinc in the ratio of 2 : 3 (both these alloys have only these elements in the solution). If the new alloy contains Aluminum and Zinc in the ratio of 3 : 5, what is the percentage of carbon in the new alloy?
1. 11.51
2. 15.78
3. 20.53
4. 22.36

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Correct Answer - Option 2 : 15.78

Calculation:

Let K and P are amounts of alloys used in the preparation of the new alloy.

⇒ Amount of Zinc in the new alloy = (K/4) + (3P/5)

⇒ Amount of Aluminum in the new alloy = 2P/5

⇒ Amount of Carbon in the new alloy = 3K/4

In the new alloy, the Amount of Aluminum and Zinc are in the ratio 3 : 5.

⇒ (2P/5)/((K/4) + (3P/5)) = 3/5

⇒ 2P = (3K/4) + (9P/5)

⇒ P/5 = 3K/4

⇒ P = 15K/4 or K = 4P/15

Percentage of Carbon in the new alloy = ((3K/4)/(K + P)) × 100

⇒ ((3K/4)/(19K/4)) × 100 = 15.78 %

In these types of problems, it is important to find the relation between the quantity of the solutions used for the preparation of the new solution.

 

If the quantity of the solutions used for the preparation for the new solution is equal, then we can calculate the volume of a component by simply taking the average of their ratios in the old mixtures.

For example:  The amount of Zinc in the new alloy = ((1/4) + (3/5))/2 = 17/40

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