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

Let's denote the following variables:

• \( n \): number of original students
• \( m \): number of new students
• \( W \): average weight of the original students (in kg)
• \( W+3 \): average weight of the new students (in kg)

Initially, the total weight of the original students is \( nW \). When new students join, the new average weight becomes \( W + 0.6 \) kg. The total weight equation for both original and new students is:

\((n+m)(W + 0.6) = nW + m(W+3)\) 

Expanding and simplifying:

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

Cancel out the common terms \( nW + mW \):

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

Simplify to find a relationship between \( n \) and \( m \):

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

\( 0.6n = 2.4m \)

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

\( n = 4m \)

This shows that the ratio of the number of original students to the number of new students is \( \frac{n}{m} = \frac{4}{1} \).

Original Students	New Students	Ratio
4	1	4:1

Answer 2

Let the initial number of students be \(n\), with an average weight of \(x\). 
Upon adding \(m\) more students, the new average weight \(= x + 3\)
Given that the average weight of the students in the class increases by \(0.6\) after the new students are added. Then,

\(\frac{nx + m(x + 3)}{n + m} = x + 0.6\)

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

\(2.4m = 0.6n\)

\(24m = 6n\)

\(\frac{n}{m} = \frac{24}{6}\)

\(\frac{n}{m} = \frac{4}{1}\)
\(n : m = 4 : 1\)

So, the correct option is (D): \(4 : 1\)