chetan2u wrote:
A retail store has 60 employees—full-time salespeople (FT sales), part-time salespeople (PT sales), and managers—in the proportions shown by the graph. Each full-time salesperson and each manager works the same number of hours per week; each part-time salesperson works exactly half that many hours per week
The store wants the ratio of the total number of hours worked per week by full-time salespeople to the total number of hours worked by part-time salespeople to be 2:3 and wants to achieve this ratio without changing the number of managers or the number of hours each manager works per week.
Based on the information provided, select the option from each drop-down menu that creates the most accurate statement.
To achieve the desired ratio, the store could [Dropdown Placeholder #1] the number of full-time salespeople and [Dropdown Placeholder #2] the number of part-time salespeople.
Of the 60 employees, 30% are FT (= 18) and 60% are PT (= 36)
FT are half in number but work twice the hours of PT so their ratio of total number of hours worked is 1:1.
We want to make it 2:3 by adding or reducing the number of FT and PT only. Since the ratio has to be reduced, we must need to decrease the number of FT and/or increase the number of PT. Keep an eye on the available options.
Say each PT works x hrs and each FT works 2x hrs.
Ratio of total number of hours worked = \(\frac{2}{3} = \frac{(18 - ?)*2x}{(36+?)*x}=\frac{(18 - ?)*2}{(36+?)}\)
Denominator should be 3 times (18 - ?).
If we reduce 18 by 2, we get 16 but denominator cannot be made 48 (no option of adding 12 PTs)
If we reduce 18 by 4, we get 14 and denominator can be made 42 by adding 6 PTs. This works.
Decrease FTs by 4 and increase PTs by 6. ANSWERThe question uses the application of concepts of ratios and percentages. Check them here:
https://youtu.be/5ODENGG5dvchttps://youtu.be/HxnsYI1Rws8
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