­A retail store has 60 employeesfull-time salespeople (FT sales), par

­This GI Pie chart question exemplifies the importance of organizing information in a table so that we do not get confused about which factor can be changed and which factor cannot be changed according to the conditions specified in the question.

Next, this question also showcases how to utilize answer choices to arrive at the answer. Through data processing, we get one equation in two variables and we need to find the answers to both these variables. Thus, for such questions, we need to use the answer choices. But for that as well, there are two approaches:
1. Plugging the choices one by one
2. Drawing inferences from the equation and then doing smart analysis with the choices

Watch the video solution to see the detailed solution. While plugging choices one by one may appear to be the faster way, in the long run as you develop your skill of drawing inferences, you will realize that it is faster to solve the question by drawing inferences and then doing smart analysis of the choices. So, invest the time in building this skill during your preparation mode.
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ckavya2691, refer your query on the question

There are 60 employees. Manager - 6; FT - 18 and PT - 36
Let each PT work for x hours, so FT will work for 2x hours.

The ratio = 18*2x:36*x = 1:1

However, this has to be changed to 2:3 by changing the number of employees.
Clearly, number of hours worked increases for PT / decreases for FT, so their PT has to be increased / FTcould be increased/decreased depending on the increase in PT.

Increase in PT:
2: 38, so number of hours = 38x....Ratio \(38x*\frac{2}{3}:38x­\).....NUmber of hours for FT is not an integer and options are in integer.
4: 40, so number of hours = 40x....Ratio \(40x*\frac{2}{3}:40x­\).....NUmber of hours for FT is not an integer and options are in integer.
6: 42, So number of hours = 42x....Ratio \(42x*\frac{2}{3}:42x = 28x:42x = 14*2x:42*x­\).....Thus, increase by 6, 36 to 42, and a simultaneous decrease of 18-14 or 4 would give a ratio 2:3.

Solution
A. Decrease by 4
B. Increase by 6
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­As per the Question - "and wants to achieve this ratio without changing the number of managers or the number of hours each manager works per week"

Therefore, the Decrease in the number of FTs should be equal to the increase in no of PTs.

On solving, Decrease and Increase come to 4.5 Each, which is not possible

IMO All options are wrong

­The question nowhere mentions that the number of employees has to be constant.

It says that the number of hours manager works should not change, and number of hours for FT and PT is related to the number of hours manager works.
You can only change the number of FT and PT to get the ratio.
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ft=18 (2h hrs)
pt=36 (h hrs)

2/3=2(18+x)/(36+y)

(18+x)/(36+y)=1/3

as 18/36 is 1/2 >1/3

lets reduce Num in steps. red by 2 should have denom of 42 (inc by 6)­

Official answer:


Does anyone have a different approach to this question? other than the already discussed or the official?­

ruis, another logical approach would be

The ratio of working hours that we want FT:PT to be is 2:3
As PT works half time, we require half the number of FT to do same work. Thus, converting the ratio to number of FT people : number of PT people = 2/2 : 3 or 1:3

Knowing this, we now know that earlier ratio of 30%:60% or 1:2 has to be brought down to 1:3.
Clearly FT has to be reduced and PT increased.

Initially, FT people = 30% of 60 or 18 and 60% of 60 or 36
Decrease: by(2,4,6) means (18-2,18-4,18-6) or (16,14,12)…..(I)
Increase: by(2,4,6) means (36+2,36+4,36+6) or (38,40,42)…..(II)

Now find a number in I and II that give you a ratio 1:3 => 14:42 is the answer
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Are there similar questions (PS, DI or DS) to practice where we go from initial an ratio to a different final ratio? Bunuel

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. ANSWER

The question uses the application of concepts of ratios and percentages. Check them here:https://youtu.be/5ODENGG5dvc
https://youtu.be/HxnsYI1Rws8
 

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