In a magnalium alloy, the ratio of magnesium and aluminium in a 72 kg alloy is 5 ∶ 4. Some amount of magnesium is extracted from the alloy and the ratio becomes 7 ∶ 8, how much magnesium is extracted?

In a magnalium alloy, the ratio of magnesium and aluminium in a 72 kg alloy is 5 ∶ 4. Some amount of magnesium is extracted from the alloy and the ratio becomes 7 ∶ 8, how much magnesium is extracted? Correct Answer 12 kg

Given:

The total quantity of alloy is 72 kg

The ratio of magnesium and aluminium is 5 ∶ 4

Calculations:

Let the extracted amount of magnesium be x

According to the question, we have

The ratio of magnesium and aluminium is 5 ∶ 4

⇒ Amount of Magnesium in the alloy = (5/9) × 72 = 40 kg

⇒ Amount of Aluminium in the alloy = (4/9) × 72 = 32 kg

According to the question,

Remaining magnesium is (40 - x) kg

Now, the new ratio is 7 ∶ 8

⇒ (40 - x)/32 = 7/8

⇒ 320 - 8x = 224

⇒ 8x = 96

⇒ x = 96/8

⇒ x = 12 kg

∴ The amount of extracted magnesium is 12 kg.