Question

The ratio of measurements of Copper , Zinc and Nickel in German silver is 4:3:2 respectively.Find out what weight (in kgs) of Zinc should be added to 54 kg of German Silver, so that the ratio of measurements become 6:5:3.
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Answer 1

Answer:

In a alloy of mass 100 kg the mass of copper, zinc, nickle will b in the ratio 5:3:2.

So let the masses of Co, Zn, Ni be 5x,3x,2x.

So,

5x+3x+2x=100

=>10x=100

=>x=100/10=10.

So 5x=5*10=50,3x=30,2x=20.

Here it is given, only mass of Ni is added to compose a new alloy of ratio 5:3:3 but the masses of Co and Zn remain intact.

As as a result 5x+3x=50+30=80 kg will remain intact.

In new ratio the ratio of Co, Zn and Ni is 5:3:3.

Let us take the masses of Co, Zn and Ni be 5y, 3y and 3y respectively.

5y+3y=80 kg(as this mass doesnt change at all)

=>8y=80=>y=80/8=10.

So 3y=3*10=30.

Earlier composition of alloy Ni had mass of 20 kg, now its 30 kg. so,the difference will give the mass of Ni added i.e 30–20=10 kg was added to give rise a ratio of 5:3:3.

10 kg

The total quantity of alloy before the addition of Nickel is 100 kg.

This 100 kg is composed of 50 kg Copper, 30 kg Zinc, and 20 kg Nickel

Now we want the new ratio to be 5:3:3 by adding some quantity of Nickel.

You can just look at it and say that the quantity of Nickel that should be added is 10 kg.

However, let us try and understand the method for complicated cases.

Let us say that 'x' kg of Nickel is added so that Nickel becomes 20 + x and the total quantity of the alloy becomes 100 + x

Now, Nickel is 3/(5 + 3 + 3) = 3/11 th of the total mixture.

=> (20 + x)/(100 + x) = 3/11

=> 220 + 11x = 300 + 3x

=> 8x = 80

=> x = 10

=> Quantity of Nickel that should be added is 10

Step-by-step explanation:

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Answer 2

Answer:

2 kg

Step-by-step explanation:

Ratio of Copper Zinc and Nickel = 4:3:2

In 54 kg of German silver = 24:18:12

(ratio = 54*4/9 : 54*3/9 : 54*2/9)

if x kg Zinc is added ratio become 6:5:3

$\frac{copper}{zinc} = \frac{24}{18 + x} = \frac{6}{5}$

$x = 2 \: kg$

$(or)$

$\frac{zinc}{nickel} = \frac{18 + x}{12} = \frac{5}{3}$

$x = 2 \: kg$

2 kg of zinc is added to German silver