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CAT 2022 Slot 1 — QA Question 14

Weighted AverageEasy

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 number of original students to the number of new students is

Answer & solution

  • A

    3 : 1

  • 4 : 1

  • C

    1 : 2

  • D

    1 : 4

Solution

Easy

This is a classic alligation: the original group and the joining group balance around the new overall average. The ratio of group sizes is the inverse ratio of their distances from that average.

1

Set up the averages in kg. Let the original average be aa. New students average a+3a+3, and the combined average rises by 0.60.6 to a+0.6a+0.6.

2

Apply alligation around the mean a+0.6a+0.6:

original is below by: (a+0.6)−a=0.6new is above by: (a+3)−(a+0.6)=2.4\begin{aligned} &\text{original is below by: }(a+0.6)-a=0.6\\ &\text{new is above by: }(a+3)-(a+0.6)=2.4 \end{aligned}
3

Take the inverse ratio of distances to get original:new\text{original}:\text{new}:

originalnew=2.40.6=41\frac{\text{original}}{\text{new}}=\frac{2.4}{0.6}=\frac{4}{1}

original:new=4:1\text{original}:\text{new}=\mathbf{4:1} — option (b).

CAT 2022 Slot 1 QA Q14: The average weight of students in a class increases by 600 gm when some new students join the class. If the av — Solution | TheCATExam