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A retail store employs only clerks and managers and the clerks earn $1

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A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 18 May 2017, 00:17
14
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (03:14) correct 28% (03:10) wrong based on 139 sessions

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A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8

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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 04 Jun 2017, 02:44
11
1
Here's the shortcut to do this question in 30 seconds!
Solution - think of this problem as an expenditure problem! there were 20 employees, $13.00 avg salary - Total expenditure is $260
4 employees are added, total employees now is 24, $14.00 avg. salary - Total expenditure is $336
Extra expenditure is $76
for the 4 clerks that are added, it's $46, remaining amount is $30 ($76-$46) and this $30 is expenditure for promotions. each promotion cost $7.5 ($19-$11.5), so divide 30 by $7.5 - you can 4. 4 clerks were promoted! Hope you will find it easier and faster!
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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 18 May 2017, 06:05
Bunuel wrote:
A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8


let x be the number of clerks who got promoted.
(1) \(\frac{(11.5C + 19M)}{(C+M)}\) = 13
(2) \(\frac{(11.5(C+4-X) + 19(M+x))}{(C+M+4)}\) = 14
(3) C+M = 20

From (1) & (3); C=16,M=4
substitute C,M into (2);x = 4
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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 18 May 2017, 11:12
1
Given:
clerks earn $11.50/hour
managers earn $19/hour

Total Number of Clerks currently working = c
Total Number of Managers currently working = m

Given

c+m=20
11.50c+19m = (c+m)13

Solving above two:

11.5c+19m = 13c+13m
6m = 1.5c
c=4m
4m+m=20

m=4
c=16

This year, 'n' clerks were promoted to manager

c= 16+4-n
m=4+n

(20-n)11.5+(4+n)19 = (20-n+4+n)14

230-11.5n+76+19n=336

7.5n = 336-306 = 30

n=4

Answer is B
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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 18 May 2017, 11:46
a+b=20(where a is number of clerks and b the number of manager)
Also 11.5a+19b=13*20=260

Solving for both the equations(19a+19b=380,11.5a+19b=260) and substracting, we will get 7.5a=120 or a=16)

Now since 4 new clerks were added and few members were promotes, we have 20-x clerks now and 4+x managers.

Also given that
11.5(20-x) + 19(4+x) = 24*14
230 + 76 + 7.5x = 336
7.5x = 30 or x=4(Option B)

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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 04 Jun 2017, 02:18
Hi Bunuel ,
Though I reached the answer, it took more than two minutes. Is there any shortcut that I might have missed?

--
Regards.
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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 04 Jun 2017, 02:44
2
Here's the shortcut to do this question in 30 seconds!
Solution - think of this problem as an expenditure problem! there were 20 employees, $13.00 avg salary - Total expenditure is $260
4 employees are added, total employees now is 24, $14.00 avg. salary - Total expenditure is $336
Extra expenditure is $76
for the 4 clerks that are added, it's $46, remaining amount is $30 ($76-$46) and this $30 is expenditure for promotions. each promotion cost $7.5 ($19-$11.5), so divide 30 by $7.5 - you can 4. 4 clerks were promoted! Hope you will find it easier and faster!
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Re: A retail store employs only clerks and managers and the clerks earn $1  [#permalink]

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New post 04 Apr 2019, 18:15
Bunuel wrote:
A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8


We can let x = the number of clerks in the store before any new hires or promotions. Thus, 20 - x = the number of managers, and we can create the equation:

(11.5x + 19(20 - x))/20 = 13

11.5x + 380 - 19x = 260

-7.5x = -120

x = 16

Therefore, there were 16 clerks and 4 managers before any new hires or promotions, and there were 24 employees after the personnel changes. Now let’s let n = the number of clerks who were promoted to manager. Since there are 4 new clerks who were hired, we can create the equation for the income of the employees:

(11.5(16 + 4 - n) + 19(4 + n))/24 = 14

230 - 11.5n + 76 + 19n = 336

7.5n = 30

n = 4

Answer: B
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Re: A retail store employs only clerks and managers and the clerks earn $1   [#permalink] 04 Apr 2019, 18:15
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