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P and Q are two alloys of zinc and tin, prepared by mixing the 2 metals in the ratio of 4 : 5 and 2 : 1 respectively. If equal quantities of these alloys are melted to form a third alloy R, then find the percentage of zinc in alloy R.
1. 55.56%
2. 58.58%
3. 65.76%
4. 75.89%

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Correct Answer - Option 1 : 55.56%

Given:

 THe 

Ratio of tin and silver in alloy A = 4 : 5

Ratio of tin and silver in alloy B = 2 : 1

Concept Used:

Required Percentage = Quantity of zinc/Total quantity of mixture × 100

Calculation:

Ratio of zinc and tin in alloy P = 4 : 5      ---- (1)

Ratio of zinc and tin in alloy Q = 2 : 1      ----(2)

Multiplying (2) by 3, we get

Ratio of zinc and tin in alloy Q = 6 : 3      ----(3)

Adding (2) and (3), we get

Ratio of zinc and tin in alloy R = (4 + 6) : (5 + 3) = 10 : 8

Percentage of zinc in alloy R = (10/(10 + 8)) × 100 = (10/18) × 100 = 55.56%

∴ The percentage of zinc in alloy R is 55.56%.

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