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 correct answer is D: 4:1
Suppose there were 'n' initial students with 'x' average weights.With 'm' additional pupils,the average weight will be x + 3 We must ascertain the value of n: m.A is provided.It is given, average weight of students in a class increased by 0.6 after new students are added.
Therefore, \(\frac{nx+m(x+3)}{n+m}\)=\(x+0.6\)
\(nx+mx+3m=mx+nx+0.6n+0.6m\)
\(2.4m=0.6n\)
\(4m=n\)
\(\frac{n}{m}=\frac{4}{1}\)

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,
\(\frac {nx+m(x+3)}{n+m}=x+0.6\)
\(nx+mx +3m = mx + nx + 0.6n + 0.6m\)
\(2.4m = 0.6n\)
\(24m = 6n\)
\(\frac nm = \frac {24}{6}\)

\(\frac nm = \frac 41\)
\(n:m=4:1\)

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