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Ratio of Original to New Students

CAT 2022 Slot 1 · Quantitative Ability · Easy · Averages

This is an easy Quantitative Ability question from the CAT 2022 Slot 1 paper. It tests Averages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    1 : 2

  2. B.

    3 : 1

  3. C.

    1 : 4

  4. D.

    4 : 1

Answer

D

Explanation

Let n1n_1 be the number of original students and n2n_2 be the number of new students. Let average weight of original students =A= A kg. Average weight of new students =A+3= A + 3 kg. Combined average weight =A+0.6= A + 0.6 kg (since 600 gm=0.6 kg600\text{ gm} = 0.6\text{ kg}).

By Alligation / Weighted Average: n1n2=(A+3)−(A+0.6)(A+0.6)−A=2.40.6=4\frac{n_1}{n_2} = \frac{(A + 3) - (A + 0.6)}{(A + 0.6) - A} = \frac{2.4}{0.6} = 4

Ratio of original students to new students =4:1= 4 : 1.

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