Percentages

[Abdulla]

A part- time employee whose hourly was increased by 25% decided to reduced the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced ?

A) 12.5%
B) 20%
C) 25%
D) 50%
E) 75%

The answer 20% , please need an explanation.

[cramya]

Since it deals with percentages pick 100 (easiest to work with on percentage problems)

Assume the eomployee worked 100 hours earning 1$ per hour

In a week he would earn $100

Hourly wages increase by 25% = 1 + 25/100 (1) = 1+ .25 = 1.25

If the new hourly wage is 1.25 the eomployee would earn 1.25 * 100 = 125 $


To get 125$ emp works 100hours
To get 100$(original salary ) how many hours does he need to work?

salary hours
125 100
100 x

x = 100/125*100 = 80 hours

Original work hours was 100 to get $100
New work hours is 80(with increased wages) to get 100$

Therefore we can see there is a 20% reduction in work hours i.e from 100 to 80

Hope this helps!

[iamcste]

A part- time employee whose hourly was increased by 25% decided to reduced the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced ?

A) 12.5%
B) 20%
C) 25%
D) 50%
E) 75%

The answer 20% , please need an explanation.

Assume

hrs 100/week, Rate 100, Income 10000

Hrs? , Rate 125 ( 25% increase), Income 10000


Hrs=10000/125=80

Decrease is to 80 hrs from 100 hrs

% decrease=(100-80)/100=20

hence 20% decrease

[jnellaz]

While I was typing this, the guys above beat me to the punch but anyway...

Let's say the part time employee makes $100 per hour (this is a good number to use when doing percent problems) and it is increased by 25 pct.
That means the person is making $125 per hour. THUS..

If the employee works 5 hours at $100 per hour they would make $500 for 5 hours.

To make the same money($500) at $125 they would only have to work 4 hours.

A decrease of 1/5 in hours or 20pct.

[Abdulla]

Nice work guys ..

Thank you