Question:hard

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

Updated On: Jan 15, 2026

  • 1:2

  • 3:1

  • 1:4

  • 4:1 

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The Correct Option is D

Solution and Explanation

The following variables are defined:

  • \( n \): count of initial students
  • \( m \): count of additional students
  • \( W \): mean weight (kg) of initial students
  • \( W+3 \): mean weight (kg) of additional students

The total weight of the initial students is \( nW \). Upon the addition of new students, the combined mean weight increases to \( W + 0.6 \) kg. The equation representing the total weight for all students is:

\((n+m)(W + 0.6) = nW + m(W+3)\)

Algebraic expansion and simplification yield:

\( nW + mW + 0.6n + 0.6m = nW + mW + 3m \)

Terms \( nW \) and \( mW \) are eliminated:

\( 0.6n + 0.6m = 3m \)

The relationship between \( n \) and \( m \) is simplified as follows:

\( 0.6n = 3m - 0.6m \)

\( 0.6n = 2.4m \)

\( n = \frac{2.4m}{0.6} \)

\( n = 4m \)

This establishes the ratio of initial students to new students as \( \frac{n}{m} = \frac{4}{1} \).

Original StudentsNew StudentsRatio
414:1
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