Question

4. Calculate the weight and the percentage of zinc in
the zinc-copper alloy being given that the latter's
alloy with 3 kg of pure zinc contains 90 per cent of
zinc and with 2 kg of 90% zinc alloy contains 84%
of zinc.​

Answer 1

Given:

First quantity = 3kg

Percentage of Zinc = 90%

Second quantity = 2kg

Percentage of Zinc = 90%

Percentage of alloy = 84%

To Find:

Weight and the percentage of zinc in  the zinc-copper alloy

Solution:

Let x : 3 , then y : 90%  

Thus, 10 : 90 – y  

(90-y)/3 = 10/x --- eq 1

In second case,  

Let x : 2 , then y : 90%

Therefore (84-y)/2 = 6/x --- eq 2

Dividing (1) and (2)  

 = 180 – 2y = 420 – 5y  

3y = 240  

y = 80

x = 30/(90-80)

= 30/10

= 3 kg

Quantity of zinc in x = 80% of x

= 0.8 × 3  

= 2.4 kg

Answer: Weight and percentage of zinc is 2.4 kg or 80%

Answer 2

• The weight and the percentage of zinc in the zinc - copper alloy is equal to 2.4 kg and 80% .

Given :-

• Alloy with 3 kg of pure zinc contains 90 per cent of zinc .
• Also, alloy with 2 kg of 90% zinc alloy contains 84% of zinc .

Solution :-

Let initially allow has zinc and copper in the ratio z : c .

when 3 kg of pure zinc is added

→ (z + 3) : c = 9 : 1

→ z + 3 = 9c

→ 9c - z = 3 ------ Eqn.(1)

also, when 2kg of alloy with 90% zinc is added :-

→ zinc added = 2 * 0.9= 1.8 kg

→ copper added = 2 - 1.8 = 0.2 kg .

Now it is given that, we gets 84% of zinc .

So,

→ (z + 1.8)/(z + c + 2) = 84/100 = 21/25

→ 25z + 45 = 21c + 21z + 42

→ 21c - 4z = 3 ------- Eqn. (2)

Multiplying Eqn.(1) by 4 and subtracting Eqn.(2) from result :-

→ 4(9c - z) - (21c - 4z) = 4*3 - 3

→ 36c - 21c + 4z - 4z = 12 - 3

→ 15c = 9

→ c = 3/5

putting c in Eqn.(1) :-

→ 9(3/5) - z = 3

→ z = (27/5) - 3

→ z = (27 - 15)/5

→ z = (12/5)

→ z = 2.4 kg (Ans.)

therefore,

→ Required % = (12/5) * 100 * (1/3) = 80% (Ans.)

Hence, the weight of zinc in zinc - copper alloy is equal to 2.4 kg and the percentage of zinc in the zinc - copper alloy is equal to 80% .

Learn more :-

Shakuntla Devi, Karl Gauss, Archimedes could do a lot of quick maths since their young ages.

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