Qs. Find the weight and percentage of zinc in a zinc-copper alloy, which when alloyed with 3 kgs of pure zinc contains 90% zinc and when alloyed with 2 kgs of 90% zinc contains 84% zinc.

A. 2.4 kg or 80%

B. 1.4 kg or 88%

C. 3.4 kg or 60%

D. 7.4 kg or 18%

The unknowns here are the weight of zinc and copper in the zinc-copper alloy. Assume these to be x and y kgs.
Write the equations for the two cases of alloying.
We will now have 2 variables and 2 equations. Solve simultaneously to get x and y.

A. 2.4 kg or 80%

Amount of zinc in the zinc-copper alloy (let’s call it alloy A)say x kg and y kg respectively.

Total weight of the alloy = (x + y) kg
When an alloy is formed with alloy A and 3 kg pure zinc, total weight of this new alloy (let’s call this alloy B ) would be 3+x+y kg, where weight of zinc = 3+x kg and y kg copper.

Also, this alloy has 90% zinc.
(3+x)/(3+x+y) = 90/100 = 0.9
=> 3 + x = 2.7 + 0.9x + 0.9y
=> x + 3 = 9y ——–(1)

Now, when alloy A is is mixed with 2 kg alloy B (which has 90% zinc, and therefore, 1.8 kg zinc and 0.2 kg copper), total weight of the alloy formed = 2+x+y kg, with weight of zinc = 1.8+x kg and weight of copper = 0.2+y kg.
Also, this new alloy has 84% zinc.
=> (1.8+x)/(2+x+y) = 84/100 = 0.84
=> 1.8 + x = 1.68 + 0.84x + 0.84y
=> 3 + 4x = 21y ——–(2)

Solving (1) and (2), we get,
x = 2.4 kg (weight of zinc in alloy A)
y = 0.6 kg (weight of copper in alloy A)
=> total weight of alloy A = 2.4 + 0.6 kg = 3 kg
=> percentage of zinc in alloy A = (2.4/3)100 = 80%
=> option (A) is correct.