Averages , Ratio and Proportion Question 2 - 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
- Apply the Alligation Framework:
Let the original average weight be w kg.
The new students have an average weight of w + 3 kg.
The combined average weight increases by 600 gm, which is exactly 0.6 kg, making the final mixture value w + 0.6 kg.
- Calculate the weight deviations:
Original group side difference:
(w + 0.6) − w = 0.6
New group side difference:
(w + 3) − (w + 0.6) = 2.4
- Find the student count ratio:
The ratio of the number of students is inversely proportional to these calculated deviation balances:
Number of Original Students(n) / Number of New Students(m) = 2.4/0.6 = 4/1 = 4 : 1
Correct Option: C
💡 FundaMakers Tip:
Avoid long multi-variable average statements like (nx + m(x + 3))/(n + m). Alligation works instantly on relative average shifts. The baseline variables completely disappear when you look at the raw distances from the mean (2.4 : 0.6), giving you the final 4 : 1 ratio directly.