Question : An alloy contains copper, zinc, and nickel in the ratio of 3 : 2 : 5 respectively. What quantity of nickel (in kg) must be added to 100 kg of this alloy to have the new ratio of copper, zinc, and nickel 3 : 2 : 6 respectively?
Option 1: 20 kg
Option 2: 10 kg
Option 3: 8 kg
Option 4: 15 kg
Correct Answer: 10 kg
Solution :
Given: An alloy contains copper, zinc, and nickel in the ratio of 3 : 2 : 5 respectively.
Let the weights of the alloy be $3x$, $2x$, and $5x$ for copper, zinc, and nickel in 100 kg.
The alloy's initial weight of 100 kg.
According to the question,
$3x+2x+5x=100$
⇒ $10x=100$
⇒ $x=10$ kg
The alloy now contains $x$ kg of nickel. So, the new nickel weight = $x$ + 20 kg.
The new ratio of copper, zinc, and nickel is 3 : 2 : 6 respectively.
The nickel's weight = 10 + 20 = 30 kg.
According to the question,
⇒ $x+20=30$
⇒ $x=10$ kg
Hence, the correct answer is 10 kg.
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