Question

A carpenter cuts off a plank $\frac{5}{12}$ of its length and then $\frac{6}{7}$ of what remains. If the remaining piece is $2\frac{1}{2}$ m long, the original length of the plank is

Answer 1

Let $x$ be the original length of the plank.

length of plank cut by carpenter first time is $\frac{5}{12}x$

length of plank after the first cut is $x-\frac{5}{12}x=\frac{7}{12}x$

length of plank cut by carpenter after second time is $\frac{7}{12}\times \frac{6}{7}x$

$=\frac{6}{12}x$

$\text{Remaining piece =original- cutting part}$

$\Rightarrow x-(\frac{5}{12}x+\frac{6}{12}x)=\frac{5}{2}$

$\Rightarrow x-\frac{11}{12}x=\frac{5}{2}$

$x=30m$