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

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, nx+m(x+3)n+m\frac{nx+m(x+3)}{n+m}=x+0.6x+0.6
nx+mx+3m=mx+nx+0.6n+0.6mnx+mx+3m=mx+nx+0.6n+0.6m
2.4m=0.6n2.4m=0.6n
4m=n4m=n
nm=41\frac{n}{m}=\frac{4}{1}
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Approach Solution -2

Let the initial number of students be nn, with an average weight of xx.
Upon adding mm more students, the new average weight =x+3= x + 3
Given that the average weight of the students in the class increases by 0.60.6 after the new students are added. Then,
nx+m(x+3)n+m=x+0.6\frac {nx+m(x+3)}{n+m}=x+0.6
nx+mx+3m=mx+nx+0.6n+0.6mnx+mx +3m = mx + nx + 0.6n + 0.6m
2.4m=0.6n2.4m = 0.6n
24m=6n24m = 6n
nm=246\frac nm = \frac {24}{6}

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

So, the correct option is (D): 4:14:1

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