Question

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

Answer 1

Let $p$ be the number of employees and $q$ be the wages per head.

Total wages$=pq$

Given that the number of employees working in a farm is increased by $25\%$.

Then the number of workers$=p+\left(\frac{25p}{100}\right)$

$=1.25p$

Reduced wages per employee$=0.75q$

So total wages $=1.25p\times 0.75q$

$=0.9375pq$

Decrease in $\%=(pq–0.9375pq)\times \frac{100}{pq}$

$=6.25\%$

Hence, the value of $x=6.25\%$.