Aptitude - Average - Discussion

12. 

The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.

[A]. 47.55 kg
[B]. 48 kg
[C]. 48.55 kg
[D]. 49.25 kg

Answer: Option C

Explanation:

Required average
= 50.25 x 16 + 45.15 x 8
16 + 8
= 804 + 361.20
24
= 1165.20
24
= 48.55

Sms said: (Sep 27, 2010)  
Very complicated and tough problem. Difficult to solve it and need more explanation.

Shree Hema said: (Feb 13, 2011)  
I cant understand. Please anyone help me ?

Jithu said: (May 21, 2011)  
See @hema

Avg=total/no
avg_weight=total_weight/no_student
here 16 boys's avg =50.25
let us take x be total
Avg=x/no
ie,50.25=x/16
so
x=50.16*25
x=804------(1)

let take y be total
then
Avg=y/no
ie,45.15=y/8
So y= 45.15*8
y==361.20--------(2)

Total_number of students is=16+8=24
So all weight=x+y
i.e,804+361.20=1165.20
avg=total/no
therefore avg=1165.20/24
Avg=48.55

Karan said: (Jul 22, 2011)  
@Jitu superb explanation.

Pavan said: (Jul 28, 2011)  
I you understand the concept then u can do like this also.. its easy too

16:8 = 2:1

then, (50.25x2 + 45.15x1) / (2+1) = 48.55

M.V.Krishna/Palvoncha said: (Sep 9, 2011)  
Avg. of 16 boys= 50.25,

weight of 16 boys=(50.25*16)=804,

avg. of 8 boys= 45.15,

weight of 8 boys=(45.15*8)=361.2,

total no. boys=24,

total weight of the boys=1165.2.

avg. weight of 24 boys=(1165.2/24)

=48.55.

Madhavi said: (Sep 20, 2011)  
@heema

It can also be solved sing the following formula:n1x1+n2x2/n1+n2....... n1=16,n2=8,x1=50.25 & x2=45.15

Swapnil said: (Nov 7, 2011)  
16 * 50.25= 804 (total wt of 16 boys)
8 * 45.15= 361.2 (total wt remaining 8 boys)
_____________________
24 = 1165.2 (total wt of all boys)
= 1165.2/24
=48.55 (Average wt of all boys)

Muneer.S said: (Sep 21, 2012)  
16 boys total weight= 50.25*16= 804kg

8 boys total weight= 45.15*8= 361.2

Total weight of all boys= 804+361.2 =1165.2
Avg weight of all boys= 1165.2/24= 48.55

Gokul Sreekumar said: (Nov 28, 2013)  
A more simple way.

Instead of doing these complex multiplications you can simply take (50.25+50.25+45.15) /3 & you will get the answer.

Vino Venkat said: (Dec 2, 2013)  
Any short cut method to this problem?

Rajwinder Singh said: (Jan 13, 2015)  
Difference between 50.25 & 45.15 is 5.1.

16*5.1 = 81.6.
81.6/24 = 3.40.
45.15+3.40 = 48.55.

Priyanka said: (Mar 5, 2015)  
How total boys 24 remaining 8 boys means? Boys inside 16 or separate 8 boys? Please explain.

Prasad said: (Oct 23, 2015)  
Why can't we take both weights as individual weights?

i.e 50.25+45.15 = 95.40.

= 95.40/2 = 47.7 kg.

This process is wrong then say what is missing?

Bhawani said: (Mar 4, 2016)  
You can also solve in this type.

16 * 50.25 + 8 * 45.15 / 24.

8 (2 * 50.25 + 45.15) / 24.

145.75 / 3.

=> 48.55

Kiran Kumar said: (Jul 13, 2016)  
This is a weighted average problem. In weighted average problem the value of the actual weights is not required. The ratio of the weights also will give you the same answer. Thus instead of 8 and 16 we can take the ratios of 8 and 16. i.e. 2 and 1 as our weights.

Bramara said: (Aug 4, 2016)  
Formula for this type of problem is (w1*x1) + (w2*x2) / (w1+w2).

Vicky said: (Aug 24, 2016)  
Is there any shortcut for this problem?

Avneet said: (Aug 30, 2016)  
16 Boys = 50.25 KG
8 Boys = 45.15 KG

Total boys and their weight is;

16B + 8B = (50.25 * 16) + (45.15 * 8).
24B = 1165.2.
B = 48.55.

Farhin Rizvi said: (Sep 12, 2016)  
As given, the average weight of 16 boys in a class = 50.25kg.

Thereby,we can write it as x1 + x2,....x16/16 = 50.25,
= x1 + x2 +.....+ x16 = 50.25 * 16 = 804.

For remaining 8 boys x1 + x2 +....+ x8/8 = 45.15,
= x1 + x2 + x3 + ........ + x8 = 45.15 * 8 = 361.2.

Thereby total number of boys = 16 + 8 = 24.
And total weight = 804 + 361.2 = 1165.2.

Average = 1165.2/24 = 48.55.

Nitin said: (Nov 15, 2016)  
Can be simply done by allegation rule.

50.25 45.15
\ /
\ /
X
/ \
/ \
2 1

NOW, (X - 45.25)/(50.25 - X) = 2/1 i.e. x = 48.55.

Shelly said: (Dec 12, 2016)  
Guys the ratio is divided in 2:1. Now use allegation method.

Bala Mayak said: (Aug 3, 2017)  
Superb, nice explanation @Pavan.

Sunita said: (Feb 9, 2018)  
Let's take X=50.25 and Y=45.15.

It's given avg of 16 mem is 50.25 so X= 16*50.25 = 804 and in the same manner 8 member Y= 45.15*8 = 361.2.

The total members are 24 therefore;
AVERAGE = (804+361.2)/24 = 48.55.

Sirisha said: (Mar 28, 2018)  
Nice trick, Thanks @Pavan.

Siddhant said: (May 6, 2018)  
Sum a/16=50.35,
Sum b/8=45.15,
Sum a=50.35*16,
Sum a=804,
Sum b=45.15*8,
Sum b=361.2.
AVG=Suma+Sumb/16+8.
AVG=801+361.2/24,
AVG=48.55.

Vijay said: (Jan 8, 2019)  
Hi, I am not getting the answer. Can anyone explain me to get it?

Shubham J said: (Jan 31, 2019)  
16 boys having avg. wt. of : 50.25, i.e 50.25 * 16 = 804.
8 boys having avg. wt. of : 45.15 i.e 45.15 * 8 = 361.2.

804+361.2=1165.2.
1165.2/24 = 48.55 (24 is total boys).

Sree Ranga said: (Sep 20, 2019)  
50.25 * 16 + 45.15 = x * 24,
804+361.2 = x * 24,
1165.2/24 = x,
X = 48.55.

Ishwar said: (Sep 5, 2020)  
The avg weight of 16 boys is 50.25, then the sum of wt of all 16 boys is 50.25 * 16 = 804.
The avg wt of remaining 8 boys is 45.15, then the sum of wt of all 8 boys is 45.15 * 8 = 361.2 .
Total boys in a class is 804+361.2 = 1165.2.
And the whole avg is 1165.2/(16+8) = 48.55.

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