Multiple choice

The number of employees working in a farm is increased by $25\%$ and the wages per head are decreased by $25\%$. If it results in $x\%$ decrease in total wages, then the value of $x$ is

  1. $0$
  2. $25$
  3. $20$
  4. $\displaystyle \frac{25}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial employees be E and wages be W. Total wages = E * W. New employees = 1.25E, new wages = 0.75W. New total = 1.25 * 0.75 * E * W = 0.9375 * E * W. The decrease is 1 - 0.9375 = 0.0625, which is 6.25% or 25/4%.

AI explanation

Using the net percentage change formula of a plus b plus ab divided by 100, substitute the percentage changes in employees and wages per head. This gives 25 minus 25 plus 25 times negative 25 divided by 100, resulting in 0 minus 6.25, which is negative 6.25 percent. The negative value denotes a decrease in the total wages, so the value of x is 25 divided by 4.

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