Question

There are two alloys of copper and zinc containing copper and zinc in the ratio of 1:2 and 3:5 respectively. If 12 Kgs. of the first alloy and 16 Kgs. of the second alloy are mixed and some more pure zinc is added, the ratio of copper to zinc in the resultant alloy becomes 2 : 5. How many Kgs. of pure zinc was added?

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Answer 1

Question:

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There are two alloys of Copper and Zinc containing Copper and Zinc in the ratio of 1:2 & 3:5 respectively. If 12 kgs of first alloy and 16 kgs of second alloy are mixed and some pure Zinc is added, the ratio of Copper to Zinc in the resultant alloy becomes 2:5. How many kgs of pure Zinc was added?

Answer:

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7 kgs

Explanation:

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Ratio and Copper & Zinc in the first alloy = 1:2

Let the mass Copper be x .

Hence, mass of Zinc = 2x

Mass of the alloy = ( x + 2x ) = 3x

Hence, In 12 kg alloy, we have-

3x = 12

x = 12/3

x = 4

Now,

Mass of Copper in 12 kg alloy = x = 4 kgs

Mass of Zinc in 12 kg alloy = 2x = 2 × 4 = 8 kgs.

Ratio of Copper & Zinc in the second alloy = 3:5

Let the mass of Copper be 3y.

Hence, mass of Zinc = 5y

Mass of the alloy = ( 3y + 5y ) = 8y

Hence, In 16 kg alloy , we have-

8y = 16

y = 16/8

y = 2

Now,

Mass of Copper in 16 kg alloy = 3y = 3 × 2 = 6 kgs

Mass of Zinc in 16 kg alloy = 5y = 5 × 2 = 10 kgs

Then,

Total Copper = ( 4 + 6 ) kgs = 10 kgs

Total Zinc = ( 8 + 10 ) kgs = 18 kgs

Let more Zinc added be x.

A/q,

10 = 2

18 + x 5

=> 10 × 5 = 2( 18 + x )

=> 50 = 36 + 2x

=> 2x = 50 - 36

=> 2x = 14

=> x = 14/2

=> x = 7

Hence, more Zinc added = x = 7 kgs.

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