In a small snack shop, the average (arithmetic mean) revenue

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