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An alloy of zinc, magnesium, and copper contains 80% of copper, 15% of zinc, and 5% of magnesium. The second alloy of copper and magnesium only is melted with the first and the mixture contains 75% of copper, 5% of zinc and 20% of magnesium. What is the percentage of magnesium in the second alloy?

An alloy of zinc, magnesium, and copper contains 80% of copper, 15% of zinc, and 5% of magnesium. The second alloy of copper and magnesium only is melted with the first and the mixture contains 75% of copper, 5% of zinc and 20% of magnesium. What is the percentage of magnesium in the second alloy? Correct Answer 27.5%

Given:

In the first alloy,

Copper = 80%

Magnesium = 5%

Zinc = 15%

In the mixture,

Copper = 75%

Magnesium = 20%

Zinc = 5%

Calculation:

In the first alloy, zinc is 15%

In the second alloy, zinc is 0%

In the mixture, zinc is 5%

By the rule of the allegation, we get

 [ alt="F6 Ujjwal Nautiyal 17-5-2021 Swati D3" src="//storage.googleapis.com/tb-img/production/21/05/F6_Ujjwal%20Nautiyal_17-5-2021_Swati_D3.png" style="width: 149px; height: 153px;">

Therefore, the first alloy and second alloy are mixed in the ratio of 1 : 2.

In the first alloy, magnesium is 5%

In the second alloy, suppose magnesium is x%

In the mixture, magnesium is 20%

By the rule of the allegation, we get

[ alt="F6 Ujjwal Nautiyal 17-5-2021 Swati D4" src="//storage.googleapis.com/tb-img/production/21/05/F6_Ujjwal%20Nautiyal_17-5-2021_Swati_D4.png" style="width: 161px; height: 155px;">

According to the question,

⇒ (x - 20) : 15 = 1 : 2

⇒ 2x - 40 = 15

⇒ 2x = 55

⇒ x = 27.5%

∴ The Magnesium in second alloy is 27.5%.

 

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