For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?
(A) 30
(B) 18
(C) 10
(D) 9
(E) 7
This is a weighted average/mixture question.
Average for the first n days = 50.
Average for today = 90.
Average for the MIXTURE of all the days = 55.
To determine the value of n, use ALLIGATION.
Step 1: Plot the 3 averages on a number line, with the average for the first n days and that for today on the ends and the average for the mixture in the middle.
50----------------55----------------90
Step 2: Calculate the distances between the averages.
50--------
5-------55--------
35------90
Step 3: Determine the ratio in the mixture.
The required ratio of 50-unit days to 90-unit days is equal to the RECIPROCAL of the distances in red.
(50-unit days) : (90-unit days) = 35:5 = 7:1.
Thus, for every 1 day with 90 units, there must be 7 days with 50 units.
Thus, today's production of 90 units requires n=7 days with 50 units.
The correct answer is
E.
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