Problem Solving

Deepthi Subbu wrote:Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting company's workforce consists of 25 percent managers, what percent of the workforce originated from Company A?

Percentage of managers in A = 10
Percentage of managers in B = 30

We can view this as an weighted average problem where 25 is the weighted average of 10 and 30. We need to find the weight of 10.

<----10-----------25-----30---->

Weight of 10 = (30 - 25)/(30 - 10) = 5/20 = 1/4

Hence, required percentage = 100/4 = 25

The correct answer is C.

Deepthi Subbu wrote:Anju@Gurome : Can you please explain this line -

Weight of 10 = (30 - 25)/(30 - 10) ?

In an weighted average, if the average of A and B is C, and weights of A and B in the average are a and b respectively, then

• aA + bB = C and (a + b) = 1

Now, b = (1 - a)

So, C = aA + (1 - a)B = B + a(A - B)
--> a = (C - B)/(A - B)

In other words, weight of A in the average = (Difference between the average and B)/(Difference between A and B)

In our case, weight of 10 = (Difference of average and 25)/(Difference between 10 and 30) = (30 - 25)/(30 - 10)

You can visualize the situation on the number line also.
<-----10-------------25-------30---->

The ratio of the weights of 10 and 30 in the average will be equal to the ratio of distances of 30 and 10 from 25, respectively.

So, (weight of 10)/(weight of 30) = (distance between 25 and 30)/(distance between 10 and 25)
--> (weight of 10)/(weight of 30) = 5/15 = 1/3
--> weight of 10 = (weight of 30)/3

Now, (weight of 10 + weight of 30) = 1

So, weight of 10 = 1/4

Hope that helps.