CAT Practice : Averages, Ratios, Mixtures

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?
    1. 100 kgs ≤ x ≤ 200 kgs
    2. 80 kgs ≤ x ≤ 240 kgs
    3. 110 kgs ≤ x ≤ 220 kgs
    4. 75 kgs ≤ x ≤ 250 kgs

 

  • Correct Answer
    Choice D. 75 kgs ≤ x ≤ 250 kgs

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

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



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Visit Piverb.com
Visit Wizako.com