CAT quant - mixtures question

1. Mixtures

2. Mixtures
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?
(a) 100 kgs < x < 200 kgs (b) 80 kgs < x < 240 kgs
(c) 110 kgs < x < 220 kgs (d) 75 kgs < x < 250 kgs

3. Mixtures
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?
Alloy 1 Tin 25 Lead 75 Total 100 kg
Alloy 2 Tin
3x
5
Lead
2x
5
x kg

4. Mixtures
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 = 25 +
3x
5
×
100
100 + x
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?

5. Mixtures
This number should be between 40% and 50%
40 < 25 +
3x
5
×
100
100 + x
< 50
Solving the inequality, x has to lie between 75 and 250 kg.
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?

6. Mixtures
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)
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?

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