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
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: Sep 17, 2024
1:2
3:1
1:4
4:1
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The Correct Option is D
Approach Solution - 1
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, \(\frac{nx+m(x+3)}{n+m}\)=\(x+0.6\)
\(nx+mx+3m=mx+nx+0.6n+0.6m\)
\(2.4m=0.6n\)
\(4m=n\)
\(\frac{n}{m}=\frac{4}{1}\)
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, \(\frac{nx+m(x+3)}{n+m}\)=\(x+0.6\)
\(nx+mx+3m=mx+nx+0.6n+0.6m\)
\(2.4m=0.6n\)
\(4m=n\)
\(\frac{n}{m}=\frac{4}{1}\)
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Approach Solution -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): \(4:1\)
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