Question
Download Solution PDFAn alloy contains 40% of silver, 30% of copper, and 30% of nickel. How much silver (in kg) should be added to 25 kg of the alloy so that the new alloy contains 50% of silver?
Answer (Detailed Solution Below)
Detailed Solution
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Silver = 40%; Copper = 30%; Nickel = 30%
Let, the total weight of alloy = 100 units
So, the silver = 40 units
If we add 20 units silver then, alloy = (100 + 20) = 120 units
also, silver = 40 + 20 = 60 units
Now, silver is 50% of the alloy [∵ silver = 60 and alloy = 120]
So, 100 units = 25 kg
⇒ 20 units = (25/100) × 20 = 5 kg
∴ A total of 5 kg silver (in kg) should be added to 25 kg of the alloy so that the new alloy contains 50% of silver.
Alternate Method
Given:
An alloy contains 40% of silver, 30% of copper, and 30% of nickel.
Total weight of the alloy = 25 kg
The required percentage of silver = 50%
Calculation:
The ratio of silver, copper and nickel = 40 : 30 : 30 = 4 : 3 : 3
Let, total silver = 4x; copper = 3x; and nickel = 3x
So, 4x + 3x + 3x = 25
⇒ 10x = 25
⇒ 4x = (25/10) × 4 = 10
The weight of silver in 25 kg = 10 kg
Suppose, the amount of silver added = a kg
Then, (10 + a) = 1/2 (25 + a) [∵ 50% = 1/2]
⇒ 20 + 2a = 25 + a
⇒ 2a - a = 25 - 20
⇒ a = 5
∴ A total of 5 kg silver (in kg) should be added to 25 kg of the alloy so that the new alloy contains 50% of silver.
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