Question

174 workers can complete a task in 15 days by working for 8 hours each day. If 145 workers have to complete the same work in 12 days, what should be the increase in the working hours for each worker?

Answer 1

$$\begin{array}{ccc}No.ofworkers& No.ofdays& Workingdays\\ 174& 15& 8\\ 145& x& 12\end{array}$$
$Workinghours\left(h\right)\propto \frac{1}{Numberofworkers\left(n\right)}$
$Workinghours\left(h\right)\propto \frac{1}{Numberofdays\left(d\right)}$

$\Rightarrow h\propto \frac{1}{nd}$

$\Rightarrow hnd=constant$

$\Rightarrow h_1{n}_1{d}_1=h_2{n}_2{d}_2$

⇒ $175\times 15\times 8=x\times 145\times 12$

⇒ $x=\frac{175\times 15\times 8}{145\times 12}$

$\therefore$ $x=12days$