A part-time employee whose hourly wage was increased by 25

Although most of the others have provided their explanations using formulae, if you are not comfortable, you can use the below to solve the problem.

Its the same as the formulaes depicted below but i guess easier to undestand.

let the employee work for $ 100 an hour and a total of 100 hours per month.

His current salary will therefore be 100*100

his salary increases by 25 % --> new salary = 125

since total salary is same
therefore 100*100 = 125 * x

where x is the new hours he needs to work to maintain his monthly inclome


calculating u find x = 80 --> the hours has decreased from 100 to 80 or a 20 % decrease

Consider this:

Total Income = Hourly Wage * No of hours
If we want to keep the total income same,

Hourly Wage * No of hours = New Hourly Wage * New No of hours
Hourly Wage * No of hours = 5/4 * Hourly Wage * New No of hours

So New No of hours/No of hours = 4/5
A decrease of 1/5 i.e. 20%

Or think of it this way:
Since total income has to remain the same, Hourly wage *No of hours has to remain the same. If Hourly wage gets multiplied by 5/4 (an increase of 25%), no of hours should be multiplied by 4/5 to keep their product same i.e. no of hours should be reduced by 1/5 i.e. 20%.

Let original hourly wage be x and let the no of hours worked be y
Total wage will be =x*y
After the increment the wage will be=1.25 x
Now we need to find number of hours worked so that

x*y=1.25x*z i.e z=4/5 y

%decrease = (y-4/5y)/y *100=100/5=20%.
Thus my answer is B.

Correct me if I am wrong.

Number of Hours he works today = N
Hourly Wage today = P


Number of Hours he works today = M
Hourly wage after increase = P + 25% = P(1+25/100) = P * (5/4)

To keep the total wage constant :
N*P = M * P * (5/4)

M / N = 4/5
(N-M) / N = 1/5 (fraction by which Number of hours can be decreased while keeping total wage same)

To get the percentage , multiply both side by 100

percent of the number of hours worked be reduced ((N-M) *100/ N) = 100/5 = 20%
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A = hours of work BEFORE wage increase
B= hours of work AFTER wage increase
when answering about increase or decrease, we need to make the denomenator being the old one.
Here we know that to get the same total wage, A must be 1.25 times of B;
(x is a multiple of #hours, it will get cancel out)

Decrease of hrs = (Bx-Ax)/Ax = (1-1.25)/1.25 = 0.2 = 20%

Let initial salary be X. Then new salary is 1.25X.
Let the initial no. of hours = h1 and final no. of hours = h2;
given:
X(h1) = 1.25X(h2)
=> h1 = 1.25(h2) (cancelling X on both sides)
We need to find the percent change in no. of hours:

Formula:
Percent change = (New - Original)/Original * 100
=> (h2 - h1)/h1 * 100
Now,
We know that h1 = 1.25(h2)
=> h2/h1 = 1/1.25;
Using dividendo;
we get (h2 - h1)/h1 = (1-1.25)/1.25 ------(1)
We get our answer by multiplying (1) with 100

Hourly Wage

Initial New

$P $125P/100

X hours <X (lets say Y)

given

PX = (125P/100)Y

=> X = (125/100)Y

% decrease = ((x - y)/x )*100


= 20%

w1 * h1 = w2 * h2

w1 * h1 = 1.25 w1 * h2 => h2 = 4 h1/ 5 = 0.8 h1 => 20% decrease

hahaha...If you read this question and are a consultant who is paid hourly wages....you will think :

Hey, my current hourly rate is 100 $. Now it has increased by 25%.I can reduce the time I work, because I am now earning more and want to spend time on some of my hobbies/free time :D

So how much % time can I work less !!!

100 $ per hr(1 hr) = 125$ per hr(new time in hrs) ==> new time = 100/125 hrs = 100/25.5 = 20/25 = 80/100
Old time = 1 hr

Time decrease = 1-80/100 = 20/100 or 20%

I am not putting any approach, just a practical way I would have seen this problem...

By far the quickest way to solve this problem is by using number plugging as the question is asking a percent in the end.

assume:
Employee initial salary = $100
Old hours: 20
New salary = $125
New hours: x

20 * 100 = x * 125
x = 16
Percent of reduction = 4/20 * 100 = 20%

Answer: B

Picking works better

100- old wage
50 - old hours
100+25=125 - new wage

50*100=125x
x=40, so 50-40*100/50=20%

B

Wage ........... No. of Hrs .................. Total

10 ...................... 10 ............................ 100 (Initially)

12.5 .................... 10 .............................. 125 (After increment of 10% wage)

12.5 ...................... x .......................... 100 (Lets say no. of hrs worked = x for 100)

\(x = \frac{100}{12.5} = 8\)

Reduction percentage \(= \frac{10-8}{10} * 100 = 20%\)

Answer = B

Hours * Wage per hour = Wage

New Wage -
Hours * 1.25 * Wage per hour = 1.25 * Wage

So, New Wage = 1.25 * Old Wage
Now, forget Hours or Wage per hour. We need to decrease New Wage to make it equal to Old Wage.
So % decrease is
(New Wage - Old Wage)/New Wage = (1.25 - 1)/1.25 = 0.25/1.25 = 1/5 = 20%

omg!!
it's really a simple math
just follow the rule.......

reduction in consumption =[( r/100+r)*100]%
=25/125*100
=20%
so, the best answer is 20%
hope it is helpful!!!

Hi Let the number of hours be in 1 week x
and his hourly wage be y
then his total weekly income will be =x*y
His hourly wage increased by 25 % then his new hourly wage will be =1.25y
But he reduces his number of hours worked to maintain same total wage , therefore we have ,
Let a% be the actual decrease in y
Then
1.25axy=xy
a=1/1.25=4/5 =80% so hours are by reduced by 20%

We can let the employee’s wage = w, the number of hours = h, and the percentage reduction = n. Thus:

wh = (1 - n/100)(w)(h)(1.25)

We can divide both sides by wh, convert 1.25 to 5/4, and re-express (1-n/100) as (100 - n)/100 to get:

1 = (100 - n)/100 x 5/4

4/5 = (100 - n)/100

400 = 5(100 - n)

80 = 100 - n

n = 20

Answer: B
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30-sec approach: By what percent must hours worked decrease so that total weekly income remains unchanged?
By 1 - (fractional inverse of the percent increase)

When the original quantity is the start and end value, percent increase and percent decrease are inversely proportional. Use a fraction for the percent increase of one factor. Flip that fraction. Subtract from 1. The result is the percent by which the other factor must decrease. Thus:

\(xy = 1\)
\(x\) increases by 25% = 1.25* = \(\frac{5}{4}\)

Flip to \(\frac{4}{5}\) and subtract from 1 to yield percent by which \(y\) must decrease:

\(1 - \frac{4}{5} = \frac{1}{5}\) = 20 percent

(Or assess the flipped fraction: \(\frac{4}{5}\) = .8 = 80 percent = 20 percent decrease)

Note: if \(xy = 1\), then

\(\frac{5}{4}x *\\
\frac{4}{5}y =\\
1\)

Longer method, w/ numbers (no need!):

x = wage per hour = $20
y = # of hours worked = 10

(Wage per hour)(# of hours) = total weekly income

Total wages = $20 * 10 = $200

x, $20, increases by 25 percent:

x = \(\frac{5}{4}(20)\) = 25. We want $200. What is y?

\((25)(y)= 200\), so \(y = 8\)

By what percent did y decrease?

\(\frac{new-old}{old} =\frac{10-8}{10} =\frac{1}{5} = .20 * 100 =\) 20%

In other words, when you want the original quantity to remain the same and one factor increases by a percent, to calculate the corresponding percent decrease, finding and flipping the fraction works.

Answer B

*An increase of 25 percent =
\(1.25 =1\frac{25}{100} = 1\frac{1}{4} = \frac{5}{4}\)
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Can someone explain why my method is wrong...I'm getting nowhere close to the correct answer:

xy = 5x/4 * [(100-y)/100] .. so solve for y here.
xy = (500x-5xy)/400
400xy = 500x-5xy
405xy = 500x
y = 500/405 = 10/9 ... but obviously this is not the answer and I can't see what mistake I made.

If I use 100 = xy to start...then I can get the answer because 5x/4 just becomes 125 but if I try to just use variables throughout the equation, I mess it up so badly. Any help please!!

How did you get 4/5y?
x*y=1.25x*z i.e z=4/5 y here