The average weight of 5 students in a class was reported to be 60kg.

Question

The average weight of  5  students in a class was reported to be  60kg . However, the average seems to be too low. So after re-examination, it was found that one student was actually  80kg  and was recorded incorrectly. After this correction, the actual average was  70kg . What was the weight which was recorded incorrectly?

A.  20kg 
 
B.  25kg 
 
C.  30kg 
 
D.  50kg 
 
E.  80kg

rajatchopra1994 · Answer

Explanation:
Avg. Weight Initially=60Kg
Total students: 5
Total Weight Initially: 60X5= 300kg
After Correction Found Average increase to 70Kg.
So New Total Weight: 70X5 = 350Kg
Weight Difference : 350-300 = 50Kg.
Weight corrected was 80kg.
So difference: 80-50 = 30Kg.

IMO-C

QuantMadeEasy · Answer

Average weight of 5 students increases by 10 kg after reexamination
Total increase in weight for 5 students is 50 kgs
Incorrect weight = correct weight - total increase in weight 
 = 80 - 50 = 30 Kgs
C is correct.

MathRevolution · Answer

=>

Assume  a, b, c, d,  and  e  are the weights of the  5  students.

Since their average is reported as  60kg , we have  \frac{(a + b + c + d + e) }{ 5} = 60  or  a + b + c + d + e = 300.

If  a  is the incorrectly recorded weight, then  \frac{(80 + b + c + d + e) }{ 5} = 70  or  80 + b + c + d + e = 350.  We have  b + c + d + e = 270.

Then,  a = (a + b + c + d + e) – (b + c + d + e) = 300 – 270 = 30.

Therefore, C is the answer.
Answer: C

ScottTargetTestPrep · Answer

Letting n = the incorrectly recorded weight, we can create the equation:

(60 x 5 - n + 80)/5 = 70

380 - n = 350

n = 30

Alternate Solution:

Using the corrected average, we find that the correct sum of the weights of the five students is 70 x 5 = 350 kg. Since the student whose weight was misreported weighs 80kg, the sum of the weights of the remaining four students is 350 - 80 = 270 kg.

Using the incorrect average, we find that the incorrect sum of the weights of the five students is 60 x 5 = 300kg. Since the sum of the weights of the four students, besides the one whose weight was misreported, is 270kg, we find the weight that was reported incorrectly is 300 - 270 = 30kg.

Answer: C

The average weight of 5 students in a class was reported to be 60kg.

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The average weight of 5 students in a class was reported to be 60kg.

Prep Toolkit

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