When we add one of the two components of an alloy to another alloy, how does the mixture change.
Mixtures - Alloys
Q.16: 100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?
100 kgs ≤ x ≤ 200 kgs
80 kgs ≤ x ≤ 240 kgs
110 kgs ≤ x ≤ 220 kgs
75 kgs ≤ x ≤ 250 kgs
Correct Answer
Choice D. 75 kgs ≤ x ≤ 250 kgs
Explanatory Answer
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Detailed Solution
Alloy 1
Tin 25
Lead 75
Total 100 kg
Alloy 2
Tin
3x/5
Lead
2x/5
x kg
The table shows the composition of the two alloys. The total percentage of tin is the total weight of the tin as a percentage of the total weight of the two alloys put together.
Percentage of Tin overall =
This number should be between 40% and 50%
40 ≤ ≤ 50
Solving the inequality, x has to lie between 75 and 250 kg.
Alternatively, we can find the range by thinking of it as two mixtures problems for the two boundary conditions.
(i) x kgs of 25% Tin mixed with 100 kgs of 60% Tin to give 40% Tin → This gives x = 75 kgs.
(ii) x kgs of 25% Tin mixed with 100 kgs of 60% Tin to give 50% Tin → This gives x = 250 kgs.
Answer choice (D)
Correct Answer: 75 kgs ≤ x ≤ 250 kgs
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