Problem Solving

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

Answer: D

Source: GMAT Prep

Given that

Average revenue over a 10 period is 400
Average revenue over the first 6 days is 360

Let the revenue per day be given by D1, D2, .... D10

Converting the above statements into equations we have

Statement (2)

\(\frac{D_1+D_2+D_3+D_4+D_5+D_6}{6}=360\)

Solving it we have

\(D_1+D_2+D_3+D_4+D_5+D_6\) = 360*6

\(D_1+D_2+D_3+D_4+D_5+D_6\) = 2160

Similarly statement (1) can be written as

\(D_1+D_2+D_3+D_4+D_5+D_6+D_7+D_8+D_9+D_10\) = 4000

Substituting the \(D_1+D_2+D_3+D_4+D_5+D_6\) value in the above equation we get

2160+\(D_7+D_8+D_9+D_10\) =4000

\(D_7+D_8+D_9+D_10\) =4000-2160

\(D_7+D_8+D_9+D_10\) = 1840

Now to find the average revenue over the last 4 days we need to divide \(D_7+D_8+D_9+D_10\) by 4

Average revenue over the last 4 days = \(\frac{D_7+D_8+D_9+D_{10}}{4}=\frac{1840}{4}=460\)

hence the OA is D