Aptitude - Average - Discussion

11. 

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

[A]. 17 kg
[B]. 20 kg
[C]. 26 kg
[D]. 31 kg

Answer: Option D

Explanation:

Let A, B, C represent their respective weights. Then, we have:

A + B + C = (45 x 3) = 135 .... (i)

A + B = (40 x 2) = 80 .... (ii)

B + C = (43 x 2) = 86 ....(iii)

Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)

Subtracting (i) from (iv), we get : B = 31.

B's weight = 31 kg.


Shree Hema said: (Feb 13, 2011)  
A+B+C=45*3=>A+B+C=135----(1)
A+B=40*2=>A+B=80----(2)
B+C=43*2=>B+C=86----(3)
Sub 3 in 1
A+86=135
A=41
Sub A value in 2 we get
41+B=80
B=31
Is this correct..
Pls anyone Reply me..

Kantha said: (Feb 21, 2011)  
Ya. Its 100% right. There will be many ways to get answers for aptitude questions. No worries.

Anil said: (Jun 29, 2011)  
A+B+C=45*3=>A+B+C=135----(1)
A+B=40*2=>A+B=80----(2)
B+C=43*2=>B+C=86----(3)
S0 80+86-135=31
B=31

Rsm said: (Jul 28, 2011)  
Anyone explain the logic behind it. Thanks in advance.

M.V.Krishna/Palvoncha said: (Sep 9, 2011)  
Hello Rsm:

Given data:

avg. of A,B,C is 45,

i.e.(A+B+C)/3=45,

=>A+B+C=135....................(1)

avg. of A,B is 40,

i.e. (A+B)/2=40,

=>A+B=80.......................(2)

avg. of B,C is 43,

i.e (B+C)/2=43,

=>B+C=86.......................(3)

from (1) & (2), we get C=55,

from (1) & (3), we get A=49,

subst. A & C in (1).

we get B=31.

Mandeep Sharma said: (Oct 23, 2011)  
so simple brother....


A+B+C= 45*3=135......1

A+B= 40*2= 80..........2

B+C= 43*2=86.......3

BY SUBTRACTING 1 FROM 2

WE GET 135-80= C=55,

THEN PUT VALUE OF C IN 3....

B=86-55= 31.

Pradeep said: (Nov 29, 2011)  
@shree hema.

You said simple method. Thanks.

Kaustubh L said: (Sep 7, 2013)  
A+B+C = 45*3 = 135---(1).

A+B = 80.

Hence (1) becomes:

80+C = 135.

C = 55.

B+C = 43*2 = 86.

B = 86-55 = 31.

Rabindra said: (Nov 12, 2013)  
Most simply answer:

We know that,

A+B+C/3 = 45.
=>A+B+C = 135 .......(i).

A+B/2 = 40 ........(a).
B+C/2 = 43 ........(b).

Add equation 'a' and 'b'.

=> (A+B/2)+(B+C/2) = 86.
=> (A+2B+C)/2 = 86.
=> A+B+C = 166 ........(ii).

Subtract equation (ii) to (i) we get value of 'B'.

B = 166 - 135 = 31.

B = 31(answer).

Ankur said: (Apr 17, 2014)  
Simplified.

Sum of weights = 45*3 = 135.
A+B+C = (45*3).
A+B = (40*2)----1.
B+C = (43*2)----2.

From 1, 80+C=135 => c=55.
from 2, B+55=86=> B=31.

Jay Jadhao said: (Apr 22, 2014)  
No * Avg = Sum.

3 * 45 = 135.
2(A,B)* 40 = 80.
2(B,C)* 43 = 86.

B= 86 - (135 - 80)= 31.

Aliyaz said: (Aug 16, 2014)  
A+B+C = 45*3.
A+B = 80.
B+C = 86.

We want 'B', So A+B+C-(A+B)-(B+C).
=> A+B+C-A-B-B-C = 135-80-86.
=> -B = -31.
=> B = 31.

Varsha said: (Sep 9, 2014)  
@Shree hema when we subtract 135-86,
Then result will be 49.

Mayur said: (Oct 6, 2014)  
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

Let A, B, C represent their respective weights. Then, we have:

A + B + C = (45 x 3) = 135 .... (i).

A + B = (40 x 2) = 80 .... (ii).

B + C = (43 x 2) = 86 ....(iii).

Adding (ii) and (iii), we get: A + B+ B + C = 80+86 .... (iv).
i.e B+A+B+C =166.

But A + B + C = 135 so B+(A+B+C)=166 i.e B+135=166 then B=166-135.
Subtracting (i) from (iv), we get : B = 31.

B's weight = 31 kg.

Priyanka said: (Aug 30, 2015)  
A+B+C = 135---- (1).

A+B = 80---- (2).
B+C = 86---- (3).

Substitute (3) in (1).

A+86 = 135.
A = 49.

Substitute A in (2).

49+B = 80.

B = 80-49.
B = 31.

Munj said: (Oct 2, 2015)  
Explained answer is perfect by using elimination method.

Nayab said: (Feb 23, 2016)  
If we add equation 1 and 3, we get 135 plus 86 = 221. So how it can be 166?

Roshan said: (Mar 1, 2016)  
When average is 45 all three so why multiply by three.

Prabakaran said: (Jul 9, 2016)  
a + b + c/3 = 45.
a + b + c = 135------>1.

We know b + c = 86.
substitute in eqn 1.

We get a + 86 = 135.
a = 49.
a + b/2 = 40.
49 + b = 80.
b = 31 //. Answer.

Avneet said: (Aug 30, 2016)  
A + B + C = 45 * 3 = 135.
A + B = 40 * 2 = 80.
B + C = 43 * 2 = 86.

Now, (A + B + C ) - (A + B) = C i.e. 55,
Vice versa for the value of A i.e. 49.

Substitute the value of A in A + B = 80.
B will be 31.

Sara said: (Sep 13, 2016)  
Thanks, @Krishna. Your explanation was useful.

Faisal said: (Mar 2, 2017)  
Thanks @Priyanka.

Anjum said: (Mar 7, 2017)  
Thanks, it is easy to access the answers.

Ayisha said: (Mar 7, 2017)  
Exactly right. Thank you all.

Anjum said: (Mar 14, 2017)  
Thanks everyone for helping it by giving the explanation.

Medha said: (Apr 13, 2017)  
B + c = 86 ( 1)
A + B + C = 135 (2)
A + B = 80 (3)

Substituting (1) in (2)
A = 135 - 86 = 49.

From (3):
B = 80 - 49 = 31.

Thorat Sandip said: (Jul 5, 2017)  
A+B+C=135......(1)
B+C=86.....(2)
SUBTRACT EQ. 2 FROM 1, WE GET.
(A+B+C)-(B+C)=135-86=49.
A=49.
A+B=80.....(3).

PUT THE VALUE OF A IN ABOVE EQUATION.
49+B=80,
B=80-49=31.

Drukyul said: (Aug 1, 2017)  
A+B+C=135.......(1)
B+C=86..............(2)
A+B=80..............(3)

A+86=135.
A=49....................(4)
Sub equ 4 in 3.
49+B=80,
B=80-49,
B=31.

Ganeshgore said: (Sep 25, 2017)  
Thanks @Kaustubh.

Raj Tiwari said: (Feb 6, 2018)  
Very easy and best trick, understand the average as equal distribution of data.

As average of A,B,C = 45.
means all is 45.

a+b is 40 , but as both should be 45, means someone took 5 from both to make them 40.
means 10 is taken so keep value -10 in mind.

Similarly for a+c = 43 , 2 is less so someone taken 2 from.both means -4 is been taken from both.

So.from both case 10 and 4.

-14 is been taken.
.
And as b is the question lets make b as the robbery and if the average should be 45 and as b taken 14 from them.

means b is 45-14 = 31.

Raja Sadhukhan said: (Aug 23, 2018)  
The average weight of A B and C is 45*3=135,
A,B is 2 person so 40*2=80,
B and C-43*2=86,
(80+86)-135,
= 31.

Dora said: (Oct 12, 2018)  
ABC is (45*3)=135,
AB is (40*2)=80,
BC is (43*2)=86.

Now;
A+B+C=135,
'-----' +C=135,
80+C=135,
C=135-80,
C=55.

So,B+C=86.
B+55=86.
B=31.

Bhuwan Joshi said: (Jan 23, 2019)  
@Shree Hema.
135-86 = 49 not 41,
than 49+ B=80,
So, B=31 Years.

Sidhu said: (Apr 18, 2019)  
A+B+C=45*3 PERSONS.
A+B=40.
B+C=43.

SO;
(A+B)+(C+B) = 40+43 = 83,
A+2B+C = 83 * 2 = 166,
B = 166 - 135 = 31.

Arpit said: (Sep 11, 2020)  
Nice solution. Thanks all.

Sandeep said: (Feb 5, 2021)  
Thanks @Shree Hema.

Sangay said: (Aug 24, 2021)  
A + B + C = 45kg = 3 * 45 = 135,
A+B=40kg=2*40 = 80.
B+C=43kg=2*43 = 86.
Therefore,
80 + 86 = 166.
166-135 = 31.

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