Multiple choice

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. 1 : 2

  2. 3 : 1

  3. 1 : 4

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let N1 be original students, N2 be new students, A1 be original average, A2 = A1 + 3. New average = (N1*A1 + N2*(A1+3)) / (N1+N2) = A1 + 0.6. Solving this: 3*N2 = 0.6*(N1+N2) => 2.4*N2 = 0.6*N1 => N1/N2 = 4/1.

AI explanation

Using the mixture and alligation method, we compare the average weight of the original students against the average weight of the new students. The overall average increases by 0.6 kg, while the new students' average is 3 kg higher than the original average. This means the ratio of the change to the new students' excess is 0.6 to 2.4. Simplifying the ratio 0.6 to 2.4 gives 1 to 4, meaning the ratio of original students to new students is 4 to 1.

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