Question

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

• A. 1:2
• B. 3:1
• C. 1:4
• D. 4:1

Answer 1

The Correct Option is D

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 Students	New Students	Ratio
4	1	4:1