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Weighted Average

by abhirup1711 » Tue Apr 01, 2014 9:11 pm
Each customer subscribes to either Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the average revenue per customer per month received by the company is $100, what percentage of company revenue comes from customers of Plan A?

Ans 56.25%

Can this sum be solved by alligation?
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by [email protected] » Tue Apr 01, 2014 10:39 pm
Hi abhirup1711,

All average formula questions can be solved with the average formula (just plug the numbers and variables into the formula). This question asks you to do MORE than just use the average formula though....

A = Number of customers for Plan A
B = Number of customers for Plan B

[75A + 175B] / [A + B] = 100

Now there's just a few algebra steps:

75A + 175B = 100A + 100B

75B = 25A

3B = A

This tells us that the number of people who bought Plan A is THREE TIMES the number of people who bought Plan B.

If B=1 and A=3 then there would be the following revenue:

1(175) + 3(75)

175 + 225 = 400 total dollars

The question asks "what percentage of revenue comes from Plan A"

225/400 = 9/16 = 56.25%

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by GMATGuruNY » Wed Apr 02, 2014 2:45 am
abhirup1711 wrote:Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the company's average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A?
25%
30%
37.5%
56.25%
75%
An alternate approach is to plug in the answers, which represent the percent of revenue from Plan A.
Let the monthly revenue = 10,000.
Since the average revenue per customer = 100, the total number of customers = sum/average = 10,000/100 = 100.

Answer choice C: 37.5% from Plan A
Total revenue from A = $3750
Total revenue from B = $6250.
Number of customers for A = 3750/75 = 50.
Number of customers for B = 6250/175 ≈ 35.
Total customers = 50+35 = 85.
Too few.
Eliminate C.

To increase the total number of customers required to yield $10,000 in monthly revenue, the number of customers purchasing the less expensive plan -- Plan A -- must INCREASE.
Thus, a HIGHER percentage of the total revenue must come from Plan A.
The value in E is easier to evaluate.

Answer choice E: 75% from Plan A
Total revenue from A = $7500.
Total revenue from B = $2500.
Number of customers for A = 7500/75 = 100.
Here, the total number of customers will EXCEED 100.
Eliminate E.

The correct answer is D.
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by GMATGuruNY » Wed Apr 02, 2014 3:02 am
abhirup1711 wrote:Each customer subscribes to either Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the average revenue per customer per month received by the company is $100, what percentage of company revenue comes from customers of Plan A?
Revenue per customer for A = 75.
Revenue per customer for B = 175.
Revenue per customer for the MIXTURE of A and B = 100.

Alligation approach:

Step 1: Plot the 3 percentages on a number line, with the costs for A and B on the ends and the percentage for the mixture in the middle.
A 75------------100------------175 B

Step 2: Calculate the distances between the percentages.
A 75-----25-----100-----75----- 175 B

Step 3: Determine the ratio in the mixture.
The ratio of A to B in the mixture is equal to the RECIPROCAL of the distances in red.
A:B = 75:25 = 3:1.

Implication:
Of every 4 customers, 3 choose Plan A, while 1 chooses Plan B.

Since the average revenue per customer is $100, the total revenue for every 4 customers = 4*100 = 400.
Since each Plan A customer pays $75, the revenue for 3 Plan A customers = 3*75 = 225.
Thus:
Of the total revenue, the percentage yielded by Plan A = 225/400 * 100 = 56.25.

More alligation problems:

https://www.beatthegmat.com/mixture-prob ... 90121.html
Last edited by GMATGuruNY on Mon Nov 24, 2014 4:18 am, edited 1 time in total.
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by Abhishek009 » Wed Apr 02, 2014 9:06 am
abhirup1711 wrote:Each customer subscribes to either Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the average revenue per customer per month received by the company is $100, what percentage of company revenue comes from customers of Plan A?
Consider the Problem carefully there are 2 different factors to consider -

1. Cost / Customer

2. Revenue / Customer


Revenue = ( Cost / Customer ) X Number of Customers

We can work out the number of customers by rule of allegation as shown in the attached figure.


From there we can work out to find the revenue per plan.

Plan A = $ 75 X 3 => $225

Plan B = $175 X 1 => $ 75

If the average revenue per customer per month received by the company is $100
Total Revenue Collected by the firm is $100 X 4 => $400

% of company revenue comes from customers of Plan A -

( Revenue from Company A / Total Revenue ) X 100 %

=> 225/400 * 100%

=>56.25%
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by Brent@GMATPrepNow » Wed Apr 02, 2014 9:09 am
abhirup1711 wrote:Each customer subscribes to either Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the average revenue per customer per month received by the company is $100, what percentage of company revenue comes from customers of Plan A?
Here's one more approach:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So, with this question, we have: Weighted average = (proportion of employees in Plan A)(group A average) + (proportion of employees in Plan A)(group B average)

Let A = % of employees in Plan A (with each employee paying $75)
This means that 100 - A = % of employees in Plan B (with each employee paying $175)
Weighted average = $100 per employee

Plug into formula to get: 100 = (A/100)(75) + [(100 - A)/100](175)
Multiply both sides by 100 to get: 10,000 = 75A + 17,500 - 175A
Rearrange to get: -7500 = -100A
Solve to get: A = 75

IMPORTANT: This means that 75% of the employees are in Plan A.

The question asks us to find the percentage of company revenue that comes from customers of Plan A.

To find this percentage, let's say that there are 100 employees at the company.
This means that 75 are in Plan A, and 25 are in Plan B.
So, revenue from Plan A = (75)($75) = $5625
Revenue from Plan B = (25)($175) = $4375
So, TOTAL revenue = $5625 + $4375 = $10,000

If the revenue from Plan A = $5625, then the percentage of revenue from Plan A = (100)$5625/$10,000
= [spoiler]56.25%[/spoiler]

For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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