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

Question

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

KrishnanTN · Answer

(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

chrisjonatan · Answer

Assume:
Sum of 9 students weight = 90
Average weight = (90 + 50)/10
 = 14

New student =
(90 + x)/10 = 14.5
x = 55

GMATWhizTeam · Answer

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 .

EgmatQuantExpert · Answer

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

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

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

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