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The average weight of 10 students is increased by half a Kg when one

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Bunuel
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The average weight of 10 students is increased by half a Kg when one [#permalink] The average weight of 10 students is increased by half a Kg when one   13 Aug 2021, 02:15
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86% (01:22) correct 14% (02:05) wrong based on 43 sessions
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The average weight of 10 students is increased by half a Kg when one of the students weighing 50 Kg is replaced by a new student. What was the weight of the new student?

(A) 60 Kg
(B) 55 Kg
(C) 45 Kg
(D) 40 Kg
(E) 35 Kg
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B
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Re: The average weight of 10 students is increased by half a Kg when one [#permalink] The average weight of 10 students is increased by half a Kg when one   13 Aug 2021, 02:25
(Sum Of 10 Weights)/10 = x
Sum of 10 Weights = 10x
(Sum of 10 weights -50 +50 + Delta )/10=x + .5
Sum of 10 Weights+ Delta = 10x + 5
--> Delta is 5
50 + 5 = 55
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Re: The average weight of 10 students is increased by half a Kg when one [#permalink] The average weight of 10 students is increased by half a Kg when one   25 Aug 2021, 00:57
Assume:
Sum of 9 students weight = 90
Average weight = (90 + 50)/10
= 14

New student =
(90 + x)/10 = 14.5
x = 55
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Re: The average weight of 10 students is increased by half a Kg when one [#permalink] The average weight of 10 students is increased by half a Kg when one   25 Aug 2021, 03:53
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Solution:

Let the average of \(10\) students be \(= x\)

So the sum of weights of these \(10\) students \(= 10x\)

We are told that when one of the students weighing \(50 Kg\) is replaced by a new student, the average increases by \(0.5\).

Inference: Since the average is increasing due to the addition of this new kid, we can be sure that this new kid is over \(50 kgs\). This leaves us with Options A and B.

Let the weight of the new kid be \(= y\).

So, according to problem, we can write: \(\frac{(10x-50+y)}{(10)}=x+0.5\)

\(⇒ 10x-50+y=10x+5\)

\(⇒ y-50=5\)

\(⇒ y=55\)

Hence the right answer is Option B.
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The average weight of 10 students is increased by half a Kg when one [#permalink] The average weight of 10 students is increased by half a Kg when one   30 Aug 2021, 05:22
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Solution



Given

    • The average weight of 10 students increases by half a kg when one of the students weighing 50 kg is replaced by a new student.

To find
    • Weight of the new student.

Approach and Working out
Let the average weight of 10 students be x kgs.
    • Thus, we have sum of the weights of 10 students = 10x kgs.
Let the weight of the new student be y kgs.
Since the average weight of 10 students increases by half a kg if the student with weight 50kgs is replaced by the one with y kgs, we have
    • \(\frac{(sum – 50 + y)}{10} = x + 0.5\)
    • \(10x – 50 + y = 10x + 5\)
    • \(y = 55 kgs\)

Thus, the weight of the new student = 55 kgs

Correct Answer: Option B
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The average weight of 10 students is increased by half a Kg when one [#permalink]
30 Aug 2021, 05:22
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Bunuel
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