Problem Solving

A part-time employee whose hourly wage was increased by 25 percent decided to reduce 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%

q/a-b can someone explain

income = wage * time. Increasing w by 25% makes the new wage 5/4 * w. To offset this change and ensure that income (w * t) remains steady, multiply t by the inverse of 5/4, so that the new time will be 4/5 * t, and the new income = the old income: 5/4 * w * 4/5 * t = w * t. The change in time (4/5) is a 20% decrease. that's why (B) is the answer.

These two percentages (25% increase and 20% decrease) are often used in this type of problem because a 4/5 and 5/4 cancel each other out neatly in multiplication.

Ankitaverma wrote:A part-time employee whose hourly wage was [color=redd]increased[/color] by 25 percent decided to reduce 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%

q/a-b can someone explain

The is a short and cute rule for solving such questions...

When 2 Quantities are related in some way and we have their product ...

Say , Total Pay = Wage / Hour * No of Hours work

Amount spent on Rice = Cost of Rice / Kg * No of Kgs Bought


And we are given a % change of a quantity then there are 2 possibilities...

Either there is an Increase or a Decrease -


Since it is a case of Increase -

As it the example presented here there is an increase of 25% (1/4 ) of Hourly wage...

Total weekly income = Hourly wage * number of hours worked

You simply have to add 1 more to the numerator and multiply by 100 to get the result..

Hence answer will be 1/5 *100 = 20%


Had it been a decrease -

Say if the problem was :


A part-time employee whose hourly wage was decrease by 25 percent decided to reduce 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?


The instead of adding 1 to the denominator we will have to subtract 1 and multiply by 100 to get the result...

The answer would have been -

1/( 4 - 1 ) *100 % =>33.33%


Plz feel free if you have any doubt , if U adopt this method U can hit the answer in the blink of an eye..