A grocery store stocker whose hourly wage was increased by 50 percent

\(\frac{100}{15} = 6.67\)

Thus, percentage reduction in hours required is 33.33%, answer will be (E)

Hi Abishek, I think you mean the answer is (D) 33.33%

The numbers of hours worked reduced from 10 to 6.67 = 33.33% reduction, (D).

Percent increase and percent decrease are inversely proportional when the original value is constant (or when returning to the original is the goal).

When there is a percent increase and decrease problem and the original is constant or sought after:

1) Find the fraction for the percent increase or decrease;

2) Flip the fraction;

3) If a percent increase is needed as offset, subtract the flipped fraction FROM 1. Change the decimal to a percent. Done. OR

4) If a percent decrease is needed as offset, subtract 1 from the flipped fraction. Change the decimal to a percent. Done.

Here, we have a 50 percent increase in weekly wage.

The worker wants to maintain the same weekly pay.

By what percent must he reduce his number of hours worked?

1) Fraction: A 50 percent increase = \(1.5 = 1 \frac{1}{2} = \frac{3}{2}\)

2) Flip that fraction: \(\frac{3}{2} --> \frac{2}{3}\)

3 ) Subtract from 1: \((1 - \frac{2}{3}) = \frac{1}{3} = .3333 \approx{33.33}\) % is the percent by which he must decrease his hours to maintain his original weekly pay.

Answer D

To offset a percent increase: (1 - fractional inverse of the increase)
To offset a percent decrease: (fractional inverse of the decrease - 1)

let the weekly Wage be W and total number of hours worked = H.
Lets say that the stocker reduced his weekly working hours by x.
So, in order to keep the total wages same
=> W * H = 1.5W *(H-x)
=> H= 1.5H -1.5x
=> 0.5H = 1.5x
=> x = 1/3 = 0.3333 = 33.33%
Hence, D

i directly considered 2/3 =66%
should have considered change - makes sense to subtract from 1

Thanks!!

We can use the % change formula for a quick solve

Old value = 150% or \frac{3}{2 }x
New Value = x

therefore: \((x-\frac{3}{2}) \frac{2}{3}= \frac{(2-3)}{3} (\frac{2}{3}) = -\frac{1}{3}\)

Answer D