There are companies A, B, and C. The table shows the average ages of

Question

There are companies A, B, and C. The table shows the average ages of the employees in A, B, C, “both A and B (A∪B),” “both B and C (B∪C)” and “both C and A (C∪A),” respectively. What is the average age of the employees in all three companies A, B and C?

Attachment:

7.23ps.png

A. 28
B. 30
C. 32
D. 34
E. 36

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Official Answer

D

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yashikaaggarwal · Accepted Answer

Let the no. Of people in Company A = X
Company B = Y
Company C = Z

Average age of company A = 41
Total age of Company A employees = 41X
Company B employees = 23Y
Company C employees = 37Z

We have to find 41x+23y+37z/x+y+z = ?

41x+23y/x+y = 33
41x+23y = 33x+33y
8x = 10y
4x = 5y --------(1)

23y+37z = 29(y+z) 
23y+37z = 29y+29z
8z = 6y
4z = 3y ----------(2)

41x+37z = 39.5(x+z) 
1.5x = 2.5z
3x = 5Z -------(3)

X:Y:Z
4:5:_
_:3:4
3:_:5

Equating all three. 
12:15:20
Value of A:B:C

Putting valeus. 
=> 41x+23y+37z/x+y+z = 
=> 41(12)+23(15)+37(20)/12+15+20 
=> 492+345+740/47
=> 1577/47
=> 33.55

Nearest to 34
Answer is D

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Rohanpipalwa · Answer

Couldn't we just find the average of A,B, & C? I did that way and got 33.33 which is the closest to 34

MathRevolution · Answer

=> 7.23ps(a).png

udaypratapsingh99 · Answer

No, because the numbers of employees in the companies are different. You know that when you observe the average of AUB - the avg is not simply avg of avg ages of A & B. Similar is the case of avg of AUC or avg of BUC. The number of employees works as weights.

So, the correct formula to calculate avg age of employees of 2 companies A & B with x & y employees respectively is: 
 => (xA + yB) / (x+y)

Dhwanii · Answer

MathRevolution ,  udaypratapsingh99 ,  yashikaaggarwal

I am getting 4x = 5y, 1.5x = 2.5 z (I continued without converting to integer), 3y = 4z 
which equals to 
x:y:z = 6:15:10
Thus, 
41(6)+23(15)+37(10)/ 6+15+10= 603.33
what is it that I'm doing wrong ? Only difference I see with my calculations and ones posted here is that I haven't converted 1.5x = 2.5z into integers, so what's the mistake ?

yashikaaggarwal · Answer

Let's see,
A:B:C
4:5:_ (multiply by 3)
_:3:4 (multiply by 5)
----------------------
12:15:_
_:15:20
-----------
12:15:20

Let's solve it another way using
1.5x:2.5z and 4x:5y

A:B:C
4:5:_ (multiply by 1.5)
1.5:_:2.5 (multiply by 4)
------------------
6:7.5:_
6:_:10
-----------------
6:7.5:10

In both cases, the average will be near about 34 after putting value.

Posted from my mobile device

udaypratapsingh99 · Answer

Hi  Dhwanii ,
What I think you're missing out is on equating the equations. Equating the equations doesn't mean simply multiplying the coefficients of corresponding variables in equations.
1. As you just need to find out the ratio, you'll need only 2 equations of those 3. Pick any two.
2. Now, in order to compare(in order to find the ratio) these two equations these equations should be on the same scale. For this, you need to make the coefficient of the common variable equal in both the equations by multiplying each equation by a certain number - the number may differ for both the equation. The easy way: take the LCM of the coefficients of the common variable and multiply each equation by the factor that makes the coefficient of the common variable in that equation equal to the calculated LCM.  ((Your current method is probably making an error here.)) 
3. Now, the ratio of the coefficient of each variable is the required ratio.

Dhwanii · Answer

Ohh yeah I can spot my mistake, thank you

SSM24 · Answer

41+23+37=101/3= 33.66 rounded to 34 is this method also ok?

bhumikaakhanna · Answer

total of each company: 41+23+37=101

total of overlaps: 33+29+39.5=101.5
Combine the totals: 101+101.5=202.5
Since there are 6 groups (3 companies + 3 overlaps),
Average Age≈202.5/6≈33.75

vasu1104 · Answer

say total numbers in A= a
in B =b
in C= c

avg age in A= 41
so sum= 41a
sum in B= 23b
sum in C= 37c

now consider A and B. avg age is 33
41a + 23b / (a+b) =33
41a +23b= 33a+ 33b
8a = 10b
b= (10/8)a

now consider B and C
23b + 37c / (b+c) =29
23b + 37c = 29b + 29c
8c = 6b
8c = 6a(10/8)
c= 6a/10

now we have b and c in the form of a.
  /  
816a/24a
34

There are companies A, B, and C. The table shows the average ages of

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There are companies A, B, and C. The table shows the average ages of

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