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If Charlie decides to cut the salary per employee at his

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If Charlie decides to cut the salary per employee at his  [#permalink]

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New post 09 Jul 2013, 01:39
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If Charlie decides to cut the salary per employee at his company by 20%, five more employees can be hired for 100,000$ than can be hired at original salary. How many individuals can be hired by Charlie at the original salary if he has 50,000$ to spend on salary.

A. 10
B. 12
C. 15
D. 16
E. 20
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Re: If Charlie decides to cut the salary per employee at his  [#permalink]

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New post 09 Jul 2013, 02:00
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Let original salary be 'X'
No. of people that can be hired on original salary using $100,000 = $100,000 / X
No. of people that can be hired on 20% less salary using $100,000 = $100,000 / (1- 20%)X = $100,000 / 0.8X
Given: ($100,000 / X) - ($100,000 / 0.8X) = 5
Solve for X=> X = 5000
No. of people that can be hired on original salary using $50,000 = $50,000 / X = $50,000 / $5000 = 10
Hence the answer 'A'
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Re: If Charlie decides to cut the salary per employee at his  [#permalink]

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New post 09 Jul 2013, 02:05
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guerrero25 wrote:
If Charlie decides to cut the salary per employee at his company by 20%, five more employees can be hired for 100,000$ than can be hired at original salary. How many individuals can be hired by Charlie at the original salary if he has 50,000$ to spend on salary.

A. 10
B. 12
C. 15
D. 16
E. 20


Backsolving works perfectly for this problem.

One can also use algebraic way:

Say the average salary is x, then we would have:

100,000/(0.8x) - 100,000/x=5 --> x=5,000 --> 50,000/5,000=10.

Answer: A.
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Re: If Charlie decides to cut the salary per employee at his  [#permalink]

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New post 09 Jul 2013, 02:19
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guerrero25 wrote:
If Charlie decides to cut the salary per employee at his company by 20%, five more employees can be hired for 100,000$ than can be hired at original salary. How many individuals can be hired by Charlie at the original salary if he has 50,000$ to spend on salary.

A. 10
B. 12
C. 15
D. 16
E. 20


Original salary = X
New salary = 0.8X (because less than 20%)

Original number of employee: N
New number of employee: N +5

Total salary = 100,000

*equation 1: \((N + 5)*0.8X = 100,000\)
*equation 2: \(N*X = 100,000\)

X = 5000
If total salary = 50,000 ==> Number of employees = 50,000/5000 = 10

Hence, A
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Re: If Charlie decides to cut the salary per employee at his  [#permalink]

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New post Updated on: 06 Mar 2014, 00:19
One can also use algebraic way:

Say the average salary is x, then we would have:

100,000/x-100,000/(0.8x)=5 --> x=5,000 --> 50,000/5,000=10

The above is coming up -ve;

\(\frac{100,000}{(0.8x)} - \frac{100,000}{x}\) = 5 ; x = 5000
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Originally posted by PareshGmat on 23 Oct 2013, 02:13.
Last edited by PareshGmat on 06 Mar 2014, 00:19, edited 1 time in total.
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Re: If Charlie decides to cut the salary per employee at his  [#permalink]

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New post 12 Feb 2014, 07:13
Backsolving works perfectly for this problem.

Here’s the deal. We know that 4/5r * q+5 = 100. Now, we r is now half (50) instead of 100. Therefore, to backsolve we need to multiply each answer choice by 2. But here’s another thing, it must be divisible by 100 since q is the number of people and must be an integer. The only answer choice that when doubled is a multiple of 100 is A. Let's check 4/5*5 * 25 = 4*25= 100.

A it is!

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Re: If Charlie decides to cut the salary per employee at his  [#permalink]

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New post 18 Aug 2018, 19:23
guerrero25 wrote:
If Charlie decides to cut the salary per employee at his company by 20%, five more employees can be hired for 100,000$ than can be hired at original salary. How many individuals can be hired by Charlie at the original salary if he has 50,000$ to spend on salary.

A. 10
B. 12
C. 15
D. 16
E. 20


We can let s = the original salary per employee and n = the number of new employees that can be hired at the original salary. . So we have:

ns = 100,000

Now, if we cut the salary by 20%, the new salary per employee is 0.8s. If we can hire 5 additional new employees at that new lowered salary, then we can hire (n + 5) new employees. Thus, we have:
(n + 5)(0.8s) = 100,000

Expanding the second equation, we have:

0.8ns + 4s = 100,000

Since ns = 100,000, we have:

0.8(100,000) + 4s = 100,000

80,000 + 4s = 100,000

4s = 20,000

s = 5,000

Since the original salary per employee is $5,000, we see that Charlie can hire 10 employees for $50,000.

Answer: A
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Re: If Charlie decides to cut the salary per employee at his &nbs [#permalink] 18 Aug 2018, 19:23
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