pzazz12 wrote:
In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days?
A. $420
B. $440
C. $450
D. $460
E. $480
This can be solved using Weighted Average concept also.
First, let's make an observation based on the given data. Average revenue of 10 days is $400 while the average revenue of first 6 days is $360, $40 less than average of 10-day period. For average revenue of first 6 days, $360, to go up to average revenue of $400 overall, the average revenue of remaining 4 days must be >$400 since the number of days left are lesser.
So, here no. of days act as weights.
Now, weighted average is calculate using the formula:
Avg. = (W1* X1 + W2*X2)/W1+W2 ---------------------- 1 ; where W1, W2 = weights ; X1, X2 = values
If you rearrange the formula in "1" you get,
W1/W2 = (X2 - Avg)/(Avg - X1) ---------- 2
Applying formula "2" in the given question, we have
w1 = 6 (days)
w2 =4 (days)
Avg = $400
X2 = a (unknown - to be calculated)
X1 = $360
Substituting values, we get
6/4 = (a - 400)/ (400-360) or 3/2 = (a-400)/40
on simplifying, we get
60 = a-400 or a = 400 + 60 = $460
So, the snack shop must make an average revenue of $460 in last 4 days in order to have overall average revenue of 10-days equal to $400