Average, Mixture and Alligation Question 1 - CAT 2022
The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is:
Step-by-Step Explanation
This problem can be solved instantly using the Alligation Method by treating the weights as deviations from the original average weight.
- Let the original average weight be W kg.
- The average weight of the new students is W + 3 kg.
- The combined average weight increases by 600 gm (0.6 kg), becoming W + 0.6 kg.
Set up the alligation cross-subtraction:
Original Students (W) New Students (W + 3)
/
/
Net (W + 0.6)
/
/
|(W + 3) − (W + 0.6)| |(W + 0.6) − W|
= 2.4 = 0.6
The ratio of the number of original students to new students is:
Ratio = 2.4 : 0.6 = 4 : 1
Correct Option: C
💡 FundaMakers Tip:
Bypassing long linear equations via Alligation saves massive amounts of time on average-based word problems. Simply look at the deviation: the new group brings an excess of 3 kg per student, but the class average only moves up by 0.6 kg. The ratio of the groups is always inversely proportional to their respective deviations from the mixture value.